Solve the system using Gaussian elimination and back-substitution

Question

Solve the system using Gaussian elimination and back-substitution



 -x + 3y −  z = -9

  x − 2y + 2z = 8

 2x −  y +  z = 7

Answer 1

-1 3 -1 | -9

1 -2 2 | 8

2 -1 1 | 7

row2 = row1+row2;

row3 = 2 * row1 + row3

-1 3 -1 | -9

0 1 1 | -1

0 5 -1 | -11

row 3 = -5 * row2 + row3

-1 3 -1 | -9

0 1 1 | -1

0 0 -6 | -6

last row ---> -6z = -6

z=1

2nd row--> y + z = -1

y + 1 = -1

y = -2

1st row ---> -x + 3y - z = -9

-x + 3(-2) - 1 = -9

-x + -6 - 1 = -9

-x + -7 = -9

-x = -2

x= 2

the solution set is (x=2, y=-2, z=1)

The check is left for you, but it checks