18.06-PS6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Removing Homework (unregistered)\n",
      "INFO: Cloning Homework from git://github.com/shashi/Homework.jl.git\n",
      "INFO: Computing changes...\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<script charset=\"utf-8\">(function ($, undefined) {\n",
       "\n",
       "    function createElem(tag, attr, content) {\n",
       "\t// TODO: remove jQuery dependency\n",
       "\tvar el = $(\"<\" + tag + \"/>\").attr(attr);\n",
       "\tif (content) {\n",
       "\t    el.append(content);\n",
       "\t}\n",
       "\treturn el[0];\n",
       "    }\n",
       "\n",
       "    // A widget must expose an id field which identifies it to the backend,\n",
       "    // an elem attribute which is will be added to the DOM, and\n",
       "    // a getState() method which returns the value to be sent to the backend\n",
       "    // a sendUpdate() method which sends its current value to the backend\n",
       "    var Widget = {\n",
       "\tid: undefined,\n",
       "\telem: undefined,\n",
       "\tlabel: undefined,\n",
       "\tgetState: function () {\n",
       "\t    return this.elem.value;\n",
       "\t},\n",
       "\tsendUpdate: undefined\n",
       "    };\n",
       "\n",
       "    var Slider = function (typ, id, init) {\n",
       "\tvar attr = { type:  \"range\",\n",
       "\t\t     value: init.value,\n",
       "\t\t     min:   init.min,\n",
       "\t\t     max:   init.max,\n",
       "\t\t     step:  init.step },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\n",
       "\telem.onchange = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this); // Initialize communication\n",
       "    }\n",
       "    Slider.prototype = Widget;\n",
       "\n",
       "    var Checkbox = function (typ, id, init) {\n",
       "\tvar attr = { type: \"checkbox\",\n",
       "\t\t     checked: init.value },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.checked;\n",
       "\t}\n",
       "\telem.onchange = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Checkbox.prototype = Widget;\n",
       "\n",
       "    var Button = function (typ, id, init) {\n",
       "\tvar attr = { type:    \"button\",\n",
       "\t\t     value:   init.label },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return null;\n",
       "\t}\n",
       "\telem.onclick = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Button.prototype = Widget;\n",
       "\n",
       "    var Text = function (typ, id, init) {\n",
       "\tvar attr = { type:  \"text\",\n",
       "\t\t     placeholder: init.label,\n",
       "\t\t     value: init.value },\n",
       "\t    elem = createElem(\"input\", attr),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.value;\n",
       "\t}\n",
       "\telem.onkeyup = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Text.prototype = Widget;\n",
       "\n",
       "    var Textarea = function (typ, id, init) {\n",
       "\tvar attr = { placeholder: init.label },\n",
       "\t    elem = createElem(\"textarea\", attr, init.value),\n",
       "\t    self = this;\n",
       "\tthis.getState = function () {\n",
       "\t    return elem.value;\n",
       "\t}\n",
       "\telem.onchange = function () {\n",
       "\t    self.sendUpdate();\n",
       "\t}\n",
       "\n",
       "\tthis.id = id;\n",
       "\tthis.elem = elem;\n",
       "\tthis.label = init.label;\n",
       "\n",
       "\tInputWidgets.commInitializer(this);\n",
       "    }\n",
       "    Textarea.prototype = Widget;\n",
       "\n",
       "    // RadioButtons\n",
       "    // Dropdown\n",
       "    // HTML\n",
       "    // Latex\n",
       "\n",
       "    var InputWidgets = {\n",
       "\tSlider: Slider,\n",
       "\tCheckbox: Checkbox,\n",
       "\tButton: Button,\n",
       "\tText: Text,\n",
       "\tTextarea: Textarea,\n",
       "\tdebug: false,\n",
       "\tlog: function () {\n",
       "\t    if (InputWidgets.debug) {\n",
       "\t\tconsole.log.apply(console, arguments);\n",
       "\t    }\n",
       "\t},\n",
       "\t// a central way to initalize communication\n",
       "\t// for widgets.\n",
       "\tcommInitializer: function (widget) {\n",
       "\t    widget.sendUpdate = function () {};\n",
       "\t}\n",
       "    };\n",
       "\n",
       "    window.InputWidgets = InputWidgets;\n",
       "\n",
       "})(jQuery, undefined);\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div id=\"interact-js-shim\">\n",
       "    <script charset=\"utf-8\">\n",
       "(function (IPython, $, _, MathJax, Widgets) {\n",
       "    $.event.special.destroyed = {\n",
       "\tremove: function(o) {\n",
       "\t    if (o.handler) {\n",
       "\t\to.handler.apply(this, arguments)\n",
       "\t    }\n",
       "\t}\n",
       "    }\n",
       "\n",
       "    var OutputArea = IPython.version >= \"4.0.0\" ? require(\"notebook/js/outputarea\").OutputArea : IPython.OutputArea;\n",
       "\n",
       "    var redrawValue = function (container, type, val) {\n",
       "\tvar selector = $(\"<div/>\");\n",
       "\tvar oa = new OutputArea(_.extend(selector, {\n",
       "\t    selector: selector,\n",
       "\t    prompt_area: true,\n",
       "\t    events: IPython.events,\n",
       "\t    keyboard_manager: IPython.keyboard_manager\n",
       "\t})); // Hack to work with IPython 2.1.0\n",
       "\n",
       "\tswitch (type) {\n",
       "\tcase \"image/png\":\n",
       "            var _src = 'data:' + type + ';base64,' + val;\n",
       "\t    $(container).find(\"img\").attr('src', _src);\n",
       "\t    break;\n",
       "\tdefault:\n",
       "\t    var toinsert = OutputArea.append_map[type].apply(\n",
       "\t\toa, [val, {}, selector]\n",
       "\t    );\n",
       "\t    $(container).empty().append(toinsert.contents());\n",
       "\t    selector.remove();\n",
       "\t}\n",
       "\tif (type === \"text/latex\" && MathJax) {\n",
       "\t    MathJax.Hub.Queue([\"Typeset\", MathJax.Hub, toinsert.get(0)]);\n",
       "\t}\n",
       "    }\n",
       "\n",
       "\n",
       "    $(document).ready(function() {\n",
       "\tWidgets.debug = false; // log messages etc in console.\n",
       "\tfunction initComm(evt, data) {\n",
       "\t    var comm_manager = data.kernel.comm_manager;\n",
       "        //_.extend(comm_manager.targets, require(\"widgets/js/widget\"))\n",
       "\t    comm_manager.register_target(\"Signal\", function (comm) {\n",
       "            comm.on_msg(function (msg) {\n",
       "                //Widgets.log(\"message received\", msg);\n",
       "                var val = msg.content.data.value;\n",
       "                $(\".signal-\" + comm.comm_id).each(function() {\n",
       "                var type = $(this).data(\"type\");\n",
       "                if (val[type]) {\n",
       "                    redrawValue(this, type, val[type], type);\n",
       "                }\n",
       "                });\n",
       "                delete val;\n",
       "                delete msg.content.data.value;\n",
       "            });\n",
       "\t    });\n",
       "\n",
       "\t    // coordingate with Comm and redraw Signals\n",
       "\t    // XXX: Test using Reactive here to improve performance\n",
       "\t    $([IPython.events]).on(\n",
       "\t\t'output_appended.OutputArea', function (event, type, value, md, toinsert) {\n",
       "\t\t    if (md && md.reactive) {\n",
       "                // console.log(md.comm_id);\n",
       "                toinsert.addClass(\"signal-\" + md.comm_id);\n",
       "                toinsert.data(\"type\", type);\n",
       "                // Signal back indicating the mimetype required\n",
       "                var comm_manager = IPython.notebook.kernel.comm_manager;\n",
       "                var comm = comm_manager.comms[md.comm_id];\n",
       "                comm.then(function (c) {\n",
       "                    c.send({action: \"subscribe_mime\",\n",
       "                       mime: type});\n",
       "                    toinsert.bind(\"destroyed\", function() {\n",
       "                        c.send({action: \"unsubscribe_mime\",\n",
       "                               mime: type});\n",
       "                    });\n",
       "                })\n",
       "\t\t    }\n",
       "\t    });\n",
       "\t}\n",
       "\n",
       "\ttry {\n",
       "\t    // try to initialize right away. otherwise, wait on the status_started event.\n",
       "\t    initComm(undefined, IPython.notebook);\n",
       "\t} catch (e) {\n",
       "\t    $([IPython.events]).on('kernel_created.Kernel kernel_created.Session', initComm);\n",
       "\t}\n",
       "    });\n",
       "})(IPython, jQuery, _, MathJax, InputWidgets);\n",
       "</script>\n",
       "    <script>\n",
       "        window.interactLoadedFlag = true\n",
       "       $(\"#interact-js-shim\").bind(\"destroyed\", function () {\n",
       "           if (window.interactLoadedFlag) {\n",
       "               console.warn(\"JavaScript required by Interact will be removed if you remove this cell or run using Interact more than once.\")\n",
       "           }\n",
       "       })\n",
       "       $([IPython.events]).on(\"kernel_starting.Kernel kernel_restarting.Kernel\", function () { window.interactLoadedFlag = false })\n",
       "   </script>\n",
       "</div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: No packages to install, update or remove\n",
      "WARNING: This version of the GnuTLS library (3.2.11) is deprecated\n",
      "and contains known security vulnerabilities. Please upgrade to a\n",
      "more recent version.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<script>(function ($) {\n",
       "        // hijack IPython's methods of all CodeCells with the required metadata\n",
       "    if (!window.Homework) {\n",
       "        var get_text = IPython.CodeCell.prototype.get_text\n",
       "        IPython.CodeCell.prototype.get_text = function () {\n",
       "            if (this.metadata && typeof(this.metadata.question) !== \"undefined\") {\n",
       "                var fn = (Homework.mode() == \"create\") ? \"new_question\" : \"attempt_prompt\";\n",
       "                return 'Homework.' + fn + '(' + [\n",
       "                                         JSON.stringify(JSON.stringify(this.metadata)),\n",
       "                                         \"begin \\n\" + get_text.call(this) +\"\\n end\"\n",
       "                                       ].join(\", \") + \")\"\n",
       "            } else {\n",
       "                console.log(\"vs\", get_text.call(this))\n",
       "                return get_text.call(this)\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var cell_to_json = IPython.CodeCell.prototype.toJSON\n",
       "        IPython.CodeCell.prototype.toJSON = function () {\n",
       "            if (this.metadata && typeof(this.metadata.question) !== \"undefined\") {\n",
       "                data = cell_to_json.call(this)\n",
       "                data.source = get_text.call(this)\n",
       "                return data\n",
       "            } else {\n",
       "                return cell_to_json.call(this)\n",
       "            }\n",
       "        }\n",
       "\n",
       "        var rename_keys = IPython.OutputArea.prototype.rename_keys;\n",
       "        IPython.OutputArea.prototype.rename_keys = function (data, key_map) {\n",
       "            data = rename_keys(data, key_map)\n",
       "\n",
       "            if (data.metadata && data.metadata.reactive) {\n",
       "                var cls = \".signal-\" + data.metadata.comm_id\n",
       "                data.html = $(cls).eq(0).html()\n",
       "            }\n",
       "            return data\n",
       "        }\n",
       "\n",
       "        var delete_cell = IPython.Notebook.prototype.delete_cell\n",
       "        IPython.Notebook.prototype.delete_cell = function (index) {\n",
       "            var i = this.index_or_selected(index);\n",
       "            var cell = this.get_selected_cell();\n",
       "            if (cell.metadata && typeof(cell.metadata.question) !== \"undefined\") {\n",
       "                alert(\"Cannot delete this cell. You need to code the answer to Question \" + \n",
       "                        cell.metadata.question + \" here.\")\n",
       "            } else {\n",
       "                // go on and delete\n",
       "                delete_cell.call(this, i)\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "\n",
       "\n",
       "    function get_question(q) {\n",
       "        var i = 0\n",
       "        var cell = IPython.notebook.get_cell(i)\n",
       "        while(cell !== null) {\n",
       "            if (cell.metadata && cell.metadata.question === q) {\n",
       "                return cell\n",
       "            }\n",
       "            cell = IPython.notebook.get_cell(i)\n",
       "            i+=1\n",
       "        }\n",
       "        return null\n",
       "    }\n",
       "\n",
       "    function mount_message(cell) {\n",
       "        if (!cell) { return }\n",
       "        var meta = cell.metadata,\n",
       "            msg = meta.msg || \"<span class='icon-terminal'></span> &nbsp; Code your answer above, hit &lt;Shift+Enter&gt;, then Submit. <span style='float: right'>\",\n",
       "            score = meta.score || 0,\n",
       "            max_score = meta.max_score || 0,\n",
       "            attempts = meta.attempts || 0,\n",
       "            max_attempts = meta.max_attempts || 0\n",
       "\n",
       "        msg += \"<span style='position:absolute; top: 0.5em; right:0.5em' class='label label-info'> Score: \"\n",
       "        if (Homework.mode() === \"answering\") {\n",
       "            msg += \"<b>\" + score + \"</b> / <b>\" + max_score + \"</b>\"\n",
       "        } else if (Homework.mode() === \"create\") {\n",
       "            msg += \"<b>\" + max_score + \"</b>\"\n",
       "        }\n",
       "\n",
       "        msg += \" &middot; Attempts: \"\n",
       "        if (Homework.mode() === \"answering\") {\n",
       "            msg += \"<b>\" + attempts + \"</b>\"\n",
       "            if (max_attempts != 0) {\n",
       "                msg += \" / <b>\" + max_attempts + \"</b>\"\n",
       "            }\n",
       "        } else if (Homework.mode() === \"create\") {\n",
       "            msg += \"<b>\" + max_attempts + \"</b>\"\n",
       "        }\n",
       "        msg += \"</span>\"\n",
       "\n",
       "        var level = meta.alert || \"info\"\n",
       "\n",
       "        msg = \"<div class='hw-msg alert alert-\" + level + \"' id='hw-msg-\" + meta.question +\n",
       "               \"' style='padding: 0.5em; margin: 0; position:relative; border-radius: 0'>\" +\n",
       "               msg + \"</div>\"\n",
       "\n",
       "        $(cell.element).find(\".hw-msg\").remove()\n",
       "        $(cell.element).find(\".input_area\").eq(0).append(msg)\n",
       "        if (cell.metadata.finished) { $(cell.element).find(\".widget-area\").hide() }\n",
       "    }\n",
       "\n",
       "    function set_meta(question, extension) {\n",
       "        console.log(\"set meta\", question, extension)\n",
       "        var cell = get_question(question)\n",
       "        for (var key in extension) {\n",
       "            if (extension.hasOwnProperty(key)) {\n",
       "                cell.metadata[key] = extension[key]\n",
       "            }\n",
       "        }\n",
       "        mount_message(cell)\n",
       "    }\n",
       "\n",
       "    function get_question_cells() {\n",
       "        var cell = IPython.notebook.get_cell(0),\n",
       "            i = 0,\n",
       "            cells = []\n",
       "        while(cell !== null) {\n",
       "            if (cell.metadata && typeof(cell.metadata.question) !== \"undefined\") {\n",
       "                var q = cell.metadata.question\n",
       "                cells.push(cell)\n",
       "            }\n",
       "            i+=1\n",
       "            cell = IPython.notebook.get_cell(i)\n",
       "        }\n",
       "        return cells\n",
       "    }\n",
       "\n",
       "    function hw_create(host, course, s, f) {\n",
       "        if(!s) {\n",
       "            s = function(result){\n",
       "                if(result.code == 0) {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Problemset created',\n",
       "                        body: \"The problem set was created. Now run <code>Homework.clear_answers()</code> to get the notebook ready for distribution.\"\n",
       "                    })\n",
       "                }\n",
       "                else {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Problemset NOT created',\n",
       "                        body: \"Non-zero result code. There was a problem saving the problem set!\"\n",
       "                    })\n",
       "                }\n",
       "            };\n",
       "        };\n",
       "        if(!f) {\n",
       "            f = function() {\n",
       "                    IPython.dialog.modal({\n",
       "                        title: 'Failure',\n",
       "                        body: \"Failed to create problem set. Are you sure you have permission to edit the course? Unexpected server error.\"\n",
       "                    })\n",
       "            };\n",
       "        };\n",
       "        console.log({\n",
       "            'mode': 'create',\n",
       "            'params': JSON.stringify(course)\n",
       "        })\n",
       "        $.ajax({\n",
       "            url: host + '/jboxplugin/hw/',\n",
       "            method: 'POST',\n",
       "            data: {\n",
       "                'mode': 'create',\n",
       "                'params': JSON.stringify(course)\n",
       "            },\n",
       "            success: s,\n",
       "            failure: f\n",
       "        })\n",
       "    }\n",
       "\n",
       "    function create_problemset(config) {\n",
       "        config = config || IPython.notebook.metadata.homework\n",
       "\n",
       "        var cells = get_question_cells()\n",
       "\n",
       "        if (!config.host) { config.host == \"\" }\n",
       "        var questions = []\n",
       "        for (var i=0, l=cells.length; i < l; i++) {\n",
       "            questions.push({\n",
       "                id:    String(cells[i].metadata.question),\n",
       "                score: cells[i].metadata.max_score,\n",
       "                attempts: cells[i].metadata.max_attempts,\n",
       "                ans:   cells[i].metadata.answer,\n",
       "                explanation: cells[i].metadata.explanation || \"\"\n",
       "            })\n",
       "        }\n",
       "\n",
       "        var course = {\n",
       "             admins: config.admins || [],\n",
       "             id: config.course,\n",
       "             problemsets: [{\n",
       "                 id: config.problemset,\n",
       "                 questions: questions\n",
       "             }]\n",
       "        }\n",
       "\n",
       "        console.log(course)\n",
       "\n",
       "        try {\n",
       "            hw_create(config.host || \"\", course)\n",
       "        } catch (e) {\n",
       "            alert(\"An error occured. Problem set not saved!\")\n",
       "        }\n",
       "   }\n",
       "\n",
       "   function clear_admin_metadata() {\n",
       "       var cells = get_question_cells()\n",
       "       for (var i=0, l=cells.length; i < l; i++) {\n",
       "           var cell = cells[i]\n",
       "           delete cell.metadata.answer\n",
       "           delete cell.metadata.msg\n",
       "           cell.metadata.finished && delete cell.metadata.finished\n",
       "           delete cell.metadata.alert\n",
       "       }\n",
       "       IPython.notebook.metadata.homework.mode = \"answering\"\n",
       "       Homework.refresh_messages()\n",
       "   }\n",
       "\n",
       "   function clear_answers() {\n",
       "       var cells = get_question_cells()\n",
       "       for (var i=0, l=cells.length; i < l; i++) {\n",
       "           var cell = cells[i]\n",
       "           cell.clear_input()\n",
       "           cell.clear_output()\n",
       "       }\n",
       "       IPython.notebook.metadata.homework.mode = \"answering\"\n",
       "       Homework.refresh_messages()\n",
       "   }\n",
       "\n",
       "    function refresh_messages(q) {\n",
       "        _.map(q ? [get_question(q)] : get_question_cells(), mount_message)\n",
       "    }\n",
       "\n",
       "    $([IPython.events]).on('notebook_loaded.Notebook', refresh_messages)\n",
       "    $([IPython.events]).on('select.Cell', refresh_messages)\n",
       "\n",
       "    setTimeout(refresh_messages, 100)\n",
       "    setTimeout(refresh_messages, 200)\n",
       "    setTimeout(refresh_messages, 400)\n",
       "    setTimeout(refresh_messages, 500)\n",
       "    setTimeout(refresh_messages, 1000)\n",
       "    setTimeout(refresh_messages, 2000)\n",
       "    setTimeout(refresh_messages, 4000)\n",
       "\n",
       "    $([IPython.events]).on('status_started.Kernel', function (data) {\n",
       "        var k = data.kernel || IPython.notebook.kernel\n",
       "        k.comm_manager.register_target(\"HomeworkData\", function (comm) {})\n",
       "    })\n",
       "    IPython.notebook && IPython.notebook.kernel &&\n",
       "        IPython.notebook.kernel.comm_manager.register_target(\"HomeworkData\", function (comm) {})\n",
       "\n",
       "    window.Homework = {\n",
       "        config: {},\n",
       "        metadata: function (field) {\n",
       "            return IPython.notebook.metadata.homework[field]\n",
       "        },\n",
       "        mode: function () {\n",
       "            return Homework.metadata(\"mode\") || \"answering\"\n",
       "        },\n",
       "        set_meta: set_meta,\n",
       "        mount_message: mount_message,\n",
       "        clear_answers: clear_answers,\n",
       "        clear_admin_metadata: clear_admin_metadata,\n",
       "        get_question: get_question,\n",
       "        get_question_cells: get_question_cells,\n",
       "        refresh_messages: refresh_messages,\n",
       "        create_problemset: create_problemset\n",
       "    }\n",
       "\n",
       "})(jQuery)\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<script>IPython.notebook.kernel.comm_manager.comms[\"04ce8bea-7e60-4072-8ea3-b4fad8f093e4\"].then(\n",
       "    function (comm) {\n",
       "        comm.send({\n",
       "            cookie: document.cookie,\n",
       "            host: IPython.notebook.metadata.homework.host,\n",
       "            course: IPython.notebook.metadata.homework.course,\n",
       "            mode: IPython.notebook.metadata.homework.mode,\n",
       "            problemset: IPython.notebook.metadata.homework.problemset\n",
       "        })\n",
       "    }\n",
       ")</script>"
      ],
      "text/plain": [
       "Html(\"<script>IPython.notebook.kernel.comm_manager.comms[\\\"04ce8bea-7e60-4072-8ea3-b4fad8f093e4\\\"].then(\\n    function (comm) {\\n        comm.send({\\n            cookie: document.cookie,\\n            host: IPython.notebook.metadata.homework.host,\\n            course: IPython.notebook.metadata.homework.course,\\n            mode: IPython.notebook.metadata.homework.mode,\\n            problemset: IPython.notebook.metadata.homework.problemset\\n        })\\n    }\\n)</script>\")"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://docs.google.com/forms/d/1uPqGeJChe0FFOsuUkdeLVbgPo9LzQEbRnS0xIzE-VGo/viewform?embedded=true\" width=\"720\" height=\"570\" frameborder=\"0\" marginheight=\"0\" marginwidth=\"0\">Loading...</iframe>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Running this cell will set up auto-grading\n",
    "# It might take a while to execute.\n",
    "\n",
    "# Please fill in the MIT id form that appears below. You only need to do this once.\n",
    "\n",
    "Pkg.rm(\"Homework\")\n",
    "Pkg.clone(\"git://github.com/shashi/Homework.jl.git\")\n",
    "\n",
    "using Homework\n",
    "\n",
    "Homework.show_mit_form()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Options{:ToggleButtons,ASCIIString}([Input{ASCIIString}] score,\"report\",\"score\",\"Score\",OptionDict({\"Score\",\"Incorrect attempts\"},{\"Score\"=>\"score\",\"Incorrect attempts\"=>\"attempts\"}),None[],None[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><tr><th></th><th>Names</th><th>total</th><th>1a</th><th>1b</th><th>1c</th><th>1d</th><th>2a</th><th>2b</th><th>3a</th><th>3b</th><th>4</th><th>5a</th><th>5b</th><th>5c</th><th>5d</th><th>5e</th><th>5f</th><th>5g</th><th>5h</th><th>6a</th><th>6b</th><th>6c</th><th>6d</th><th>7a</th><th>7b</th><th>8</th><th>9a</th><th>9b</th><th>9c</th><th>10a</th><th>10b</th><th>10c</th><th>11a</th><th>11b</th><th>11c</th><th>11d</th></tr><tr><th>1</th><td>MAX</td><td><span style=\"color: black\">50.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">5.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td></tr></table>"
      ],
      "text/plain": [
       "1x36 DataFrame\n",
       "| Row | Names | total                 | 1a                     |\n",
       "|-----|-------|-----------------------|------------------------|\n",
       "| 1   | \"MAX\" | Colored(\"black\",50.0) | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 1b                     | 1c                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 1d                     | 2a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 2b                     | 3a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 3b                     | 4                      |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 5a                     | 5b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"0.5\") |\n",
       "\n",
       "| Row | 5c                     | 5d                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"0.5\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 5e                     | 5f                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"0.5\") | Colored(\"black\",\"0.5\") |\n",
       "\n",
       "| Row | 5g                     | 5h                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 6a                     | 6b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 6c                     | 6d                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 7a                     | 7b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 8                      | 9a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"5.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 9b                     | 9c                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 10a                    | 10b                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 10c                    | 11a                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 11b                    | 11c                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 11d                    |\n",
       "|-----|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") |"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "comm_id": "16550db4-20b8-4fc0-a09a-8fe8f9b93490",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Homework.progress()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 1. Determinants"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1a) (1pt.) Let A and B be any two r×r square matrices for some r.\n",
    "\n",
    "If A is not invertible then AB is not invertible. (true/false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "1a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1b) (1pt.) The determinant of A is always the product of its pivots. (true/false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "1b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1c) (1pt.) The determinant of A−B always equals detA − detB (true/false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "1c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1d) AB and BA must have the same determinant. (true/false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "1d"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 2. Placing Zeroes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2a) (2pt.) What is the smallest number of zeroes that one can place in a 4 by 4 matrix A to guarantee that detA = 0? (Int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "2a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2b) (2 pt.) What is the largest number of zeroes that one can place in a 4 by 4 matrix A while still having detA≠0? (Int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "2b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 3. Computing the Inverse of a Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3a) (2 pt.) Find A$^{-1}$ from the cofactor formula C$^T$/detA.\n",
    "\n",
    "$A = \\left( \\begin{array}\\\\ 1 & 2 & 0 \\\\ 0 & 3 & 0 \\\\ 0 & 7 & 1 \\end{array} \\right)$\n",
    "\n",
    "(Format [a b c; d e f;g h i], use p//q for fractions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "3a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3b) (2 pt.) Find A$^{-1}$ from the cofactor formula C$^T$/detA.\n",
    "\n",
    "$A = \\left( \\begin{array}\\\\ 2 & -1 & 0 \\\\ -1 & 2 & -1 \\\\ 0 & -1 & 2 \\end{array} \\right)$\n",
    "\n",
    "(Format [a b c; d e f;g h i], use p//q for fractions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "3b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 4. Maximum Determinant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2 pts.) What is the maximum determinant of a 4 by 4 matrix with entries all 1 or −1?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "4"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 5. Computing Eigenvalues and Eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5a.) (1pts) \n",
    "\n",
    "$A= \\left( \\begin{array} \\\\ -1 & 3 \\\\ 2 & 0 \\end{array} \\right)$\n",
    "\n",
    "What are the eigenvalues of A?  <br>\n",
    "        (Format: [$\\lambda_1, \\lambda_2]$  ints with $\\lambda_1<\\lambda_2$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "5a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5b) (1pt)\n",
    "What is  the eigenvector with eigenvalue $\\lambda_1$?\n",
    "\n",
    "(Format: [p,q] ints with p>0 and p and q have no common factors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 0.5,
    "question": "5b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5c) (0.5pt) What is the eigenvector with eigenvalue $λ_2$?\n",
    "\n",
    "(Format: [p,q] ints with p>0 and p and q have no common factors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 0.5,
    "question": "5c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5d) (0.5 pts) What are the eigenvalues of $A^2$? <br>\n",
    "(Format: [$\\lambda_1, \\lambda_2]$  ints with $\\lambda_1<\\lambda_2$)  (These  $\\lambda_1,\\lambda_2$ different from 5a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "5d"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5e) (0.5pts)\n",
    "What is the eigenvector of $A^2$ with eigenvalue $\\lambda_2$ where $\\lambda_1<\\lambda_2$ are the eigenvalues of $A^2$?\n",
    "\n",
    "(Format: [p,q] ints with p>0 and p and q have no common factors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 0.5,
    "question": "5e"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5f) (0.5pts)\n",
    "What is  the eigenvector of $A^2$ with eigenvalue $\\lambda_1$?\n",
    "\n",
    "(Format: [p,q] ints with p>0 and p and q have no common factors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 0.5,
    "question": "5f"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5g) (1 pt)\n",
    "Let A now be any 2 by 2 matrix. Then A$^2$ has the same ________ as A.\n",
    "\n",
    "1. eigenvalues <br>\n",
    "2. eigenvectors <br>\n",
    "3. determinant <br>\n",
    "4. characteristic polynomial \n",
    "\n",
    "(Format: 1,2,3,or 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "5g"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5h) (1 pt) When A has eigenvalues λ$_1$ and λ$_2$, A$^2$ has trace\n",
    "\n",
    "1. λ$_1$  + λ$_2$ <br>\n",
    "2. 2 λ$_1$  λ$_2$ <br>\n",
    "3.  (λ$_1$  + λ$_2$)$^2$ <br>\n",
    "4.  λ$_1^2$  + λ$_2^2$\n",
    "\n",
    "(Format: 1,2,3, or 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "5h"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 6. Extracting Information from Eigenvalues\n",
    "\n",
    "A 3 by 3 matrix B is known to have eigenvalues 0, 1, 2.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6a) (1 pt) What is the rank of B?\n",
    "\n",
    "1. 1 <br>\n",
    "2. 2 <br>\n",
    "3. 3 <br>\n",
    "4. Can not be determined\n",
    "\n",
    "(Format: 1,2,3, or 4 from the choice numbers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "6a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6b) (1 pt) What is the determinant of B$^T$B ?\n",
    "\n",
    "\n",
    "1. 0 <br>\n",
    "2. 1 <br>\n",
    "3. 4 <br>\n",
    "4. Can not be determined\n",
    "\n",
    "(Format: 1,2,3, or 4 from the choice numbers, e.g. an answer of 3 means the determinant is 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "6b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6c) (1 pt) What are the eigenvalues of B$^T$B ?\n",
    "\n",
    "\n",
    "1. 0,1,2 <br>\n",
    "2. 0,1,4 <br>\n",
    "3. 0,1,1  <br>\n",
    "4. Can not be determined\n",
    "\n",
    "(Format: 1,2,3, or 4 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "6c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6d) (1 pt) What are the eigenvalues of  $(B^2+I)^{-1}$?  (I is the 3x3 Identity)\n",
    "\n",
    "\n",
    "1. 0, 1/2, 1 <br>\n",
    "2. 1/5, 1/2, 1 <br>\n",
    "3. 1,2,5 <br>\n",
    "4. Can not be determined\n",
    "\n",
    "(Format: 1,2,3, or 4 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "6d"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 7. Companion Matrices\n",
    "\n",
    "Choose the last rows of A and B to give eigenvalues 4,7 and 1,2,3:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7a) (1 pt) $ A = \\left( \\begin{array} \\\\ 0 & 1 \\\\ * & * \\end{array} \\right) $\n",
    "\n",
    "Enter the last row of A to give eigenvalues 4,7 (Format: [a,b] ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "7a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7b) (1 pt) $ B = \\left( \\begin{array} \\\\ 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\  * & * & * \\end{array} \\right) $\n",
    "\n",
    "Enter the last row of B  to give eigenvalues 1,2,3 (Format: [a,b,c] ints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "7b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 8. Determinant Formulas with Symbolic Julia"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning: error initializing module Plots:\n",
      "Base.MethodError(f=warn, args=(\"You don't have any of the supported backends installed!  Chose from \", Array{Symbol, 1}[:qwt, :gadfly, :unicodeplots, :pyplot, :immerse, :winston]))\n"
     ]
    }
   ],
   "source": [
    "using SymPy; #Takes a while to load, and comes with lots of ignorable warnings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{bmatrix}x_{11}&x_{12}&x_{13}&x_{14}\\\\x_{21}&x_{22}&x_{23}&x_{24}\\\\x_{31}&x_{32}&x_{33}&x_{34}\\\\x_{41}&x_{42}&x_{43}&x_{44}\\end{bmatrix}"
      ],
      "text/plain": [
       "4x4 Array{Sym,2}\n",
       "[x11  x12  x13  x14]\n",
       "[                  ]\n",
       "[x21  x22  x23  x24]\n",
       "[                  ]\n",
       "[x31  x32  x33  x34]\n",
       "[                  ]\n",
       "[x41  x42  x43  x44]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Make a pretty symbolic matrix\n",
    "X(n)=Sym[\"x$i$j\" for i=1:n, j=1:n]\n",
    "X(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bigdet (generic function with 1 method)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Quick and dirty big determinant formula\n",
    "parity(p) = int(det(eye(length(p))[p,:]))\n",
    "bigdet(M) = sum([parity(p) * prod([M[i,p[i]] for i=1:size(M,1)])  for p in permutations(1:size(M,1))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x_{11} x_{22} - x_{12} x_{21}$$"
      ],
      "text/plain": [
       "x11*x22 - x12*x21"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bigdet(X(2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x_{11} x_{22} x_{33} - x_{11} x_{23} x_{32} - x_{12} x_{21} x_{33} + x_{12} x_{23} x_{31} + x_{13} x_{21} x_{32} - x_{13} x_{22} x_{31}$$"
      ],
      "text/plain": [
       "x11*x22*x33 - x11*x23*x32 - x12*x21*x33 + x12*x23*x31 + x13*x21*x32 - x13*x22*\n",
       "x31"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bigdet(X(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$x_{11} x_{22} x_{33} x_{44} - x_{11} x_{22} x_{34} x_{43} - x_{11} x_{23} x_{32} x_{44} + x_{11} x_{23} x_{34} x_{42} + x_{11} x_{24} x_{32} x_{43} - x_{11} x_{24} x_{33} x_{42} - x_{12} x_{21} x_{33} x_{44} + x_{12} x_{21} x_{34} x_{43} + x_{12} x_{23} x_{31} x_{44} - x_{12} x_{23} x_{34} x_{41} - x_{12} x_{24} x_{31} x_{43} + x_{12} x_{24} x_{33} x_{41} + x_{13} x_{21} x_{32} x_{44} - x_{13} x_{21} x_{34} x_{42} - x_{13} x_{22} x_{31} x_{44} + x_{13} x_{22} x_{34} x_{41} + x_{13} x_{24} x_{31} x_{42} - x_{13} x_{24} x_{32} x_{41} - x_{14} x_{21} x_{32} x_{43} + x_{14} x_{21} x_{33} x_{42} + x_{14} x_{22} x_{31} x_{43} - x_{14} x_{22} x_{33} x_{41} - x_{14} x_{23} x_{31} x_{42} + x_{14} x_{23} x_{32} x_{41}$$"
      ],
      "text/plain": [
       "x11*x22*x33*x44 - x11*x22*x34*x43 - x11*x23*x32*x44 + x11*x23*x34*x42 + x11*x2\n",
       "4*x32*x43 - x11*x24*x33*x42 - x12*x21*x33*x44 + x12*x21*x34*x43 + x12*x23*x31*\n",
       "x44 - x12*x23*x34*x41 - x12*x24*x31*x43 + x12*x24*x33*x41 + x13*x21*x32*x44 - \n",
       "x13*x21*x34*x42 - x13*x22*x31*x44 + x13*x22*x34*x41 + x13*x24*x31*x42 - x13*x2\n",
       "4*x32*x41 - x14*x21*x32*x43 + x14*x21*x33*x42 + x14*x22*x31*x43 - x14*x22*x33*\n",
       "x41 - x14*x23*x31*x42 + x14*x23*x32*x41"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bigdet(X(4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "\\begin{bmatrix}x_{11}&x_{12}&x_{13}&x_{14}\\\\x_{11}&x_{12}&x_{13}&x_{14}\\\\x_{31}&x_{32}&x_{33}&x_{34}\\\\x_{41}&x_{42}&x_{43}&x_{44}\\end{bmatrix}"
      ],
      "text/plain": [
       "4x4 Array{Sym,2}\n",
       "[x11  x12  x13  x14]\n",
       "[                  ]\n",
       "[x11  x12  x13  x14]\n",
       "[                  ]\n",
       "[x31  x32  x33  x34]\n",
       "[                  ]\n",
       "[x41  x42  x43  x44]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y=copy(X(4)) # Y is a copy of X(4)\n",
    "Y[2,:]=Y[1,:] # Set the second row to be equal to the first row\n",
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$0$$"
      ],
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Notice what happens if the two first rows of a matrix are identical\n",
    "bigdet(Y)\n",
    "# You might try to find the terms that cancel when for example x₂₁=x₁₁, etc.\n",
    "# I find them hard to spot: here's one x11 x22 x33 x44 - x12 x21 x33 x44 (since x21->x11 and x22->x12 )\n",
    "# Ultimately there are 24 terms which may be grouped as 12 pairs \n",
    "# which will cancel when the first two rows are identical"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Note: different from MITx **\n",
    "\n",
    "We'd be happy if you thought a bit more about determinants.\n",
    "\n",
    "Create a matrix Z whose 2nd row is equal to the sum of the 2nd row of X(4) and the first row of X(4). How does Z's determinant compare to the determinant of X(4)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "Z=X(4)\n",
    "Z[2,:]=???\n",
    "Z\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 5,
    "question": "8"
   },
   "outputs": [],
   "source": [
    "# (5 pts)\n",
    "# After defining Z, run this cell and evaluate your answer\n",
    "# Submit this cell without editing\n",
    "#(I know this seems lame, but i don't love the matlab problem in mitx either)\n",
    "\n",
    "\n",
    "simplify(bigdet(X(4)) - bigdet(Z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem 9. Areas, determinants, and fun with manipulate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that you have a matrix A which takes the basis vectors e$_1$=(1,0) and e$_2$=(0,1)  that lie along the square to the corresponding vectors Ae$_1$=(s,s),Ae$_2$=(t,0) on the parallelogram.  Julia lets your draw the pictures nicely. Have fun watching s and t vary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO: Loading help data...\n",
      "INFO: Loading additional PyPlot commands for graphing for SymPy objects:\n",
      "contour, quiver, plot_surface, plot_parametric_surface, and plot_implicit.\n",
      "See ?sympy_plotting for some more details\n"
     ]
    }
   ],
   "source": [
    "using PyPlot  #Ignore warnings\n",
    "using Interact"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 1.7,\"s\",1.7,0.5:0.1:3.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 1.2,\"t\",1.2,0.5:0.1:2.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f82e6c82250>)"
      ]
     },
     "execution_count": 94,
     "metadata": {
      "comm_id": "2e8b99e4-d80c-47a0-9af3-77d42cb0c988",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=figure(figsize=(6,6))\n",
    "\n",
    "@manipulate for s=.5:.1:3, t=.5:.1:2; withfig(f) do\n",
    "\n",
    "Ae1=[s s]\n",
    "Ae2=[t 0]\n",
    "\n",
    "subplot(221)\n",
    "ax = gca()\n",
    "arrow(0,0,0,1,head_width=0.05, head_length=0.1,color=\"g\")\n",
    "arrow(0,0,1,0,head_width=0.05, head_length=0.1,color=\"b\")\n",
    "        ax[:add_patch](matplotlib[:patches][:Rectangle]((0, 0), 1,1,facecolor=\"lightblue\"))\n",
    "axis([-.1,3,-.1,3]);\n",
    "        text(1.1,-.05,\"e₁\",horizontalalignment=\"left\",verticalalignment=\"bottom\")\n",
    "        text(.05,1.1,\"e₂\",horizontalalignment=\"center\",verticalalignment=\"bottom\")\n",
    "\n",
    "subplot(222)\n",
    "        \n",
    "ax = gca()\n",
    "arrow(0,0,Ae1...,head_width=0.05, head_length=0.1,color=\"g\")\n",
    "        arrow(0,0,Ae2...,head_width=0.05, head_length=0.1,color=\"b\")\n",
    "        ax[:add_patch](matplotlib[:patches][:Polygon]([[0 0], Ae2, Ae1+Ae2 ,Ae1],facecolor=\"lightblue\",hatch=\"*\"))\n",
    "axis([-.1,3,-.1,3]);\n",
    "        title(\"Ae₁=[$t,0] \\n Ae₂=[$s,$s]\")\n",
    "        text(t+.12,-.05,\"Ae₁\",horizontalalignment=\"left\",verticalalignment=\"bottom\")\n",
    "        text(s,.1+s,\"Ae₂\",horizontalalignment=\"center\",verticalalignment=\"bottom\")\n",
    "    end\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9a) (1 pt.) When s=1 and t=2, what is the area of the parallelogram, computed through basic geometry?  (base times height which is perpendicular to the base) (int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "question": "9a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9b) (2 pts.) When s=1 and t=2, what is the the matrix A? <br> Format: By Rows: [[a b],[c d]] all ints.  <br>\n",
    "or by cols: [[a,b] [c,d]] .  (I prefer by cols for this one, don't forget the space in the middle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "9b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "9c) (2 pts.) What is the dterminant of A? (int).  Take a moment to explain to yourself what is going on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "9c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Problem 10. Volumes and determinants"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using PyPlot\n",
    "using Interact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose that you have a matrix A which takes the following basis vectors e$_1$=(1,0,0)$^T$,e$_2$=(0,1,0)$^T$,e$_3$=(0,0,1)$^T$ that lie along the unit cube (not drawn) to the corresponding vectors Ae$_1$=(0.5,−0.5,0)$^T$,Ae$_2$=(0,0,1)$^T$,Ae$_3$=(0.5,1.5,0)$^T$ on the parallelopiped.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f83280338d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject <mpl_toolkits.mplot3d.art3d.Text3D object at 0x7f82e922d810>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=figure(figsize=(4,4))\n",
    "Ae₁=[0.5,-0.5,0]\n",
    "Ae₂=[0,0,1]\n",
    "Ae₃=[.5,1.5,0]\n",
    "z=zeros(3)\n",
    "plot3(v,w)=plot3D([ [v[i],w[i]] for i=1:3]...)\n",
    "plot3(z,Ae₁)\n",
    "plot3(z,Ae₂)\n",
    "plot3(z,Ae₃)\n",
    "plot3(Ae₁,Ae₁+Ae₂)\n",
    "plot3(Ae₃,Ae₃+Ae₂)\n",
    "plot3(Ae₂,Ae₁+Ae₂)\n",
    "plot3(Ae₂,Ae₃+Ae₂)\n",
    "plot3(Ae₁,Ae₁+Ae₃)\n",
    "plot3(Ae₃,Ae₁+Ae₃)\n",
    "plot3(Ae₁+Ae₃,Ae₁+Ae₂+Ae₃)\n",
    "plot3(Ae₁+Ae₂,Ae₁+Ae₂+Ae₃)\n",
    "plot3(Ae₃+Ae₂,Ae₁+Ae₂+Ae₃)\n",
    "text3D(.4,-.35,0,\"(.5,-.5,0)\")\n",
    "text3D(.25,1.1,0,\"(.5,1.5,0)\")\n",
    "text3D(-.1,-.2,1.1,\"(0,0,1)\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10a) (2 pt) What is the volume of the parallelopiped?  (Use area of base times height)\n",
    "\n",
    "(Format: Answer as Int!!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "10a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10b) (2 pt) What is the matrix A?\n",
    "\n",
    "format(3x3 Array{Float64,2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "10b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "10c) (1pt) What is det(A)?\n",
    "\n",
    "(Format: Answer as Int e.g. int(det(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "question": "10c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Problem 11. Area of a hexagon, determinants and fun with manipulate\n",
    "In this question, you are tasked with finding a matrix A which takes the hexagon in the first image and transforms it into the hexagon in the second image. To help you find such a matrix, look at the first image. Let e$_1$=(0,1)$^T$ be the blue horizontal vector. We define the red vector v to be the vector which forms an equilateral triangle with the first vector. Then in the second image we have Ae$_1$=(s,2)$^T$, Av=(0,4)$^T$ and we\n",
    "want you to manipulate the triangle until has angles 30, 30, and 120."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Slider{Float64}([Input{Float64}] 1.5,\"s\",1.5,0.0:0.05:3.0)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Figure(PyObject <matplotlib.figure.Figure object at 0x7f82e6362a90>)"
      ]
     },
     "execution_count": 92,
     "metadata": {
      "comm_id": "4059c108-c7ff-47c0-993e-d00e5247c716",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f=figure(figsize=(8,8))\n",
    "\n",
    "@manipulate for s=.0:.05:3; withfig(f) do\n",
    "\n",
    "hexagon=[ cos(2π*(0:5)/6)  sin(2π*(0:5)/6)]\n",
    "e₁=[1,0]\n",
    "v=[cos(π/3), sin(π/3)]\n",
    "\n",
    "subplot(221)\n",
    "ax = gca()\n",
    "arrow(0,0,e₁...,head_width=0.05, head_length=0.1,color=\"b\")\n",
    "arrow(0,0,v..., head_width=0.05, head_length=0.1,color=\"r\")\n",
    "ax[:add_patch](matplotlib[:patches][:Polygon](hexagon,facecolor=\"lightblue\"))\n",
    "text(1.1,-.05,\"e₁\")\n",
    "text(.05+v...,\"v\")\n",
    "text( .1*(v+e₁)..., \"60°\")\n",
    "axis([-2,2,-2,2]);\n",
    "\n",
    "A=  [[s, 2] [0,4]]/[e₁ v]\n",
    "        \n",
    "subplot(222)\n",
    "ax = gca()\n",
    "arrow(0,0,(A*e₁)...,head_width=0.05, head_length=0.1,color=\"b\")\n",
    "arrow(0,0,(A*v)..., head_width=0.05, head_length=0.1,color=\"r\")\n",
    "text((.05+A*e₁)...,\"Ae₁\")\n",
    "text((.05+A*v)...,\"Av\")\n",
    "ang =  int(round(acosd(dot(A*v,A*e₁)/(norm(A*v)*norm(A*e₁))),0))\n",
    "        \n",
    "text( .05,1.1, \"$(ang)°\",fontsize=8)\n",
    "text( .05,3, \"$(ang)°\",fontsize=8)\n",
    "        text(([-1 -.03]'+A*e₁)...,\"$(180-2*ang)°\",fontsize=8)\n",
    "        \n",
    "ax[:add_patch](matplotlib[:patches][:Polygon]((A*hexagon')',facecolor=\"lightblue\"))\n",
    "        title(\"Ae₁=($s,2) \\n Av=(0,4)\")\n",
    "axis([-5,5,-5,5])       \n",
    "\n",
    "\n",
    "end\n",
    "end\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11a) (1 pt.) What is the area of the first hexagon?  (Hint, the formula is $(3/2)*s^2*\\sqrt{3}$)\n",
    "\n",
    "Format: Float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "precision": 3,
    "question": "11a"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11b) (1 pt.) What is the area of the second hexagon?  (Hint: the correct hexagon is made up of 6 congruent triangles)\n",
    "\n",
    "Format: a number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "precision": 3,
    "question": "11b"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11c) (2 pt.) What is the matrix A?\n",
    "\n",
    "format: Array{Float64, 2}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 2,
    "precision": 3,
    "question": "11c"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "11d) (1 pt.) What is the determinant of A? (Notice the ratio of the hexagon areas computed in parts b and a)\n",
    "\n",
    "Format: Float64"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "attempts": 0,
    "collapsed": false,
    "max_attempts": 1000,
    "max_score": 1,
    "precision": 3,
    "question": "11d"
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [],
      "text/plain": [
       "Options{:ToggleButtons,ASCIIString}([Input{ASCIIString}] score,\"report\",\"score\",\"Score\",OptionDict({\"Score\",\"Incorrect attempts\"},{\"Score\"=>\"score\",\"Incorrect attempts\"=>\"attempts\"}),None[],None[])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table class=\"data-frame\"><tr><th></th><th>Names</th><th>total</th><th>1a</th><th>1b</th><th>1c</th><th>1d</th><th>2a</th><th>2b</th><th>3a</th><th>3b</th><th>4</th><th>5a</th><th>5b</th><th>5c</th><th>5d</th><th>5e</th><th>5f</th><th>5g</th><th>5h</th><th>6a</th><th>6b</th><th>6c</th><th>6d</th><th>7a</th><th>7b</th><th>8</th><th>9a</th><th>9b</th><th>9c</th><th>10a</th><th>10b</th><th>10c</th><th>11a</th><th>11b</th><th>11c</th><th>11d</th></tr><tr><th>1</th><td>MAX</td><td><span style=\"color: black\">50.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">0.5</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">5.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">2.0</span></td><td><span style=\"color: black\">1.0</span></td></tr></table>"
      ],
      "text/plain": [
       "1x36 DataFrame\n",
       "| Row | Names | total                 | 1a                     |\n",
       "|-----|-------|-----------------------|------------------------|\n",
       "| 1   | \"MAX\" | Colored(\"black\",50.0) | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 1b                     | 1c                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 1d                     | 2a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 2b                     | 3a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 3b                     | 4                      |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 5a                     | 5b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"0.5\") |\n",
       "\n",
       "| Row | 5c                     | 5d                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"0.5\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 5e                     | 5f                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"0.5\") | Colored(\"black\",\"0.5\") |\n",
       "\n",
       "| Row | 5g                     | 5h                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 6a                     | 6b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 6c                     | 6d                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 7a                     | 7b                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 8                      | 9a                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"5.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 9b                     | 9c                     |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 10a                    | 10b                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 10c                    | 11a                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"1.0\") |\n",
       "\n",
       "| Row | 11b                    | 11c                    |\n",
       "|-----|------------------------|------------------------|\n",
       "| 1   | Colored(\"black\",\"2.0\") | Colored(\"black\",\"2.0\") |\n",
       "\n",
       "| Row | 11d                    |\n",
       "|-----|------------------------|\n",
       "| 1   | Colored(\"black\",\"1.0\") |"
      ]
     },
     "execution_count": 11,
     "metadata": {
      "comm_id": "9a59c180-7722-47d2-8926-e7da2fa09326",
      "reactive": true
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Homework.progress()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "homework": {
   "course": "MIT-18.06-Spring-2015",
   "mode": "answering",
   "problemset": "pset6"
  },
  "kernelspec": {
   "display_name": "Julia 0.3.11",
   "language": "julia",
   "name": "julia-0.3"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.3.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}