Question

Write the augmented matrix for the following system of linear equations. Solve the equation (x,y,z) by row reduction.

x+3y-2z=5

3x+5y+6z=7

2x+4y+3z=8

Answer 1

Rewrite the system in matrix form and solve it by Gaussian Elimination (Gauss-Jordan elimination)

	1	3	-2	5
	3	5	6	7
	2	4	3	8

from 2; 3 rows we subtract the 1-th row, multiplied respectively by 3; 2

	1	3	-2	5
	0	-4	12	-8
	0	-2	7	-2

devide the 2-th row by -4

	1	3	-2	5
	0	1	-3	2
	0	-2	7	-2

from 1; 3 rows we subtract the 2-th row, multiplied respectively by 3; -2

	1	0	7	-1
	0	1	-3	2
	0	0	1	2

from 1; 2 rows we subtract the 3-th row, multiplied respectively by 7; -3

	1	0	0	-15
	0	1	0	8
	0	0	1	2

	x1 = -15
	x2 = 8
	x3 = 2