Solving System of Linear Equations

Understanding the code structure

This code is divided into the following source code files:

• main.c
• matrix.c
• util.c
• rref.c
• nullspace.c

The header files are:

• matrix.h
• util.h

Additional files are:

• LICENSE
• makefile

To build the code and run

make
./main.out

Program flow

The main contents of each file are as follows:

• Contains the main driver code
• The main function first asks the user to input the dimensions and the matrices A and b.
• The main function then calls the solve function defined in rref.c which returns a structure aug mat which is defined in matrix.h which returns the Reduced Row Echelon Form of matrix A and values of the pivots.
• Then we calculate the nullspace of the matrix by using the results returned in the above step. This is done by the nullspace function defined under nullspace.c.
• We can use these results to determine the nature of the solution by using the solution function defined in rref.c.

Sample Input and Output

Enter A:
a(11) a(12) ... a(1n)
.....................
a(n1) a(n2) ... a(nn)
Enter row and column seperated by space (E.g. 3 3): 3 4
Enter elements of a particular row in the same row itself or the program may exit
with Segmentation Fault
1 2 2 2
2 4 6 8
3 6 8 10


Enter b:
For solving a system of linear equations,
Enter the number of columns of b should be 1
b(11) b(12) ... b(1n)
.....................
b(n1) b(n2) ... b(nn)
Enter row and column seperated by space (E.g. 3 3): 3 1
Enter elements of a particular row in the same row itself or the program may exit
with Segmentation Fault
5
4
3
The pivots are:
	0	2

	1.00	2.00	0.00	-2.00	|	11.00
	0.00	0.00	1.00	2.00	|	-3.00
	0.00	0.00	0.00	0.00	|	-6.00



Nullspace of the equation is:
	-2.00	2.00
	1.00	0.00
	-0.00	-2.00
	0.00	1.00

Ax = b has No Solution