Solve the linear system by GaussJordan elimination 3x1 2x2

Solve the linear system by Gauss-Jordan elimination 3x_1 + 2x_2 - x_3 = -15 5x_1 + 3x_2 + 2x_3 = 0 3x_1 + x_2 + 3x_3 = 11 6x_1 - 4x_2 + 2x_3 = 30

Solution

Solution:

Consider the augmented matrix

Make the pivot in the 1st column by dividing the 1st row by 3

Multiply the 1st row by 5

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by 3

Subtract the 1st row from the 3rd row and restore it

Multiply the 1st row by 6

Subtract the 1st row from the 4th row and restore it

Find the pivot in the 2nd column (inversing the sign in the whole row) and swap the 3rd and the 2nd rows

Multiply the 2nd row by 2/3

Subtract the 2nd row from the 1st row and restore it

Multiply the 2nd row by -1/3

Subtract the 2nd row from the 3rd row and restore it

Multiply the 2nd row by -8

Subtract the 2nd row from the 4th row and restore it

Make the pivot in the 3rd column by dividing the 3rd row by 7/3

Multiply the 3rd row by 7/3

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by -4

Subtract the 3rd row from the 2nd row and restore it

Multiply the 3rd row by -28

Subtract the 3rd row from the 4th row and restore it

Thus system is inconsistent.

	X1	X2	X3	b
1	3	2	-1	-15
2	5	3	2	0
3	3	1	3	11
4	6	-4	2	30