Evaluate system of equations , all are one under a bracket

Question

use Cramer's rule to solve this system if equations. Use cofactors to evaluate the determinants. {-2x+y-z=7

                       2y+3z=1

                       X-3y=-8}

Answer 1

Stack the equations:

-2x + 1y -1z = 7

0x +2y +3z = 1

1x - 3y +0z = -8

Form the matrices:

(-2)------1-------(-1)----------------------x-----------------------------7

0---------2---------3----- TIMES--------y--- EQUALS-------------1

1-------(-3)--------0-----------------------z---------------------------(-8)

Take the principal determinant as:

-2[2×0 − 3×-3] − 0[1×0 − -1×-3] + 1[1×3 − 2×-1] or -13.

The determinant to find x is:

7[2×0 − 3×-3] − 1[1×0 − -1×-3] + -8[1×3 − 2×-1] or 26.

The determinant to find y is:

-2[1×0 − 3×-8] − 0[7×0 − -1×-8] + 1[7×3 − 1×-1] or -26.

The determinant to find z is:

-2[2×-8 − 1×-3] − 0[1×-8 − 7×-3] + 1[1×1 − 7×2] or 13.

Then obtain {x, y, z} as {26/-13, -26/-13, 13/-13} or {-2, 2, -1}.