Solve using Gauss Jordan elimination

Question

3) −x − 5y + z = 17

−5x − 5y + 5z = 5

2x + 5y − 3z = −10

Answer 1

-1 -5 1 17

-5 -5 5 5

2 5 -3 -10

-row1; row2/-5

=================

1 5 -1 -17

1 1 -1 -1

2 5 -3 -10

-row2 + row1; -2*row2+row3

===============================

0 4 0 -16

1 1 -1 -1

0 3 -1 -8

row 1 says 4y = -16 ---> y = -4

row 3 says 3y - z = -8

3(-4) - z = -8

-12 -z = -8

-z = 4

z = -4

row 2 says:

x + y - z = -1

x + -4 - (-4) = -1

x = -1

solution is {x=-1, y=-4, z = -4}