Gauss elimination

Solution of system of equation by Gauss elimination

Solution of system of equation by Gauss elimination

In order to apply Gauss elimination method, we need to express linear equations in matrix form AX=B, where A is called Coefficient matrix and B Right hand side vector.

Arrange matrices A and B in augmented matrix.

Now, use elementary row operations to reduced to upper traingular form.

Exchanging or swapping two rows

Adding the certain multiple of one row to another row

Multiplying a row by non-zero number

This procedure is repeated until the augmented matrix is reduced to upper triangular form

Now by back substitution the values of the variables can be found.

Example : By Gauss Elimination method, solve

x + y + z = 9

2x - 3y + 4z = 13

3x + 4y + 5z = 40

Enter matrix A : [1,1,1;2,-3,4;3,4,5]

A =

1 1 1

2 -3 4

3 4 5

Enter rhs vector B : [9;13;40]

1.0000 1.0000 1.0000 9.0000

0 -5.0000 2.0000 -5.0000

0 0 2.4000 12.0000

Solution =

1

3

5