Question

Solve the linear system by Gaussian elimination. 2x+2y+2z= 0 –2x+5y+2z= 1 8x+ y+4z=–1

Answer 1

Augmented matrix for given system of equations

Gaussian elimination

Your matrix

	X1	X2	X3	b
1	2	2	2	0
2	-2	5	2	1
3	8	1	4	-1

Make the pivot in the 1st column by dividing the 1st row by 2

	X1	X2	X3	b
1	1	1	1	0
2	-2	5	2	1
3	8	1	4	-1

Eliminate the 1st column

	X1	X2	X3	b
1	1	1	1	0
2	0	7	4	1
3	0	-7	-4	-1

Make the pivot in the 2nd column by dividing the 2nd row by 7

	X1	X2	X3	b
1	1	1	1	0
2	0	1	4/7	1/7
3	0	-7	-4	-1

Eliminate the 2nd column

	X1	X2	X3	b
1	1	0	3/7	-1/7
2	0	1	4/7	1/7
3	0	0	0	0

Solution set:

x = -1/7 - (3/7)t

y = 1/7 - (4/7)t

z = t

t = free