Solve the system of equations using matrices. use gaussian elimination with back-substitution. x + y + z = -5 x - y + 3z = -1 4x + y + z = -2

In augmented matrix form, the system is equivalent to

Subtract row 1 from row 2, and 4(row 1) from row 3:

Divide through row 2 by -2, and through row 3 by -3:

Subtract row 2 from row 3:

Divide through row 3 by 2:

The last row tells you . Then

and