solve system of linear equation using matrix method

Question

x + y -z = -6

3x - y +z = 2

x - 2y +4z =43

Answer 1

1 1 -1 -6

3 -1 1 2

1 -2 4 43

-3*row1 + row2;

-row1+ row3

1 1 -1 -6

0 -4 4 20

0 -3 5 49

-3*row2; 4*row3

1 1 -1 -6

0 12 -12 -60

0 -12 20 196

row2+row3 = row3

1 1 -1 -6

0 12 -12 -60

0 0 8 136

8z = 136

z = 136/8 = 17

12y - 12z = -60

y - z = -5

y - 17 = -5

y = 12

x +y-z = -6

x + 12 - 17 = -6

x - 5 = -6

x = -1