Question

Use Cramer's Rule to find the determinant of the coefficient matrix of this system of equations.

Answer 1

Determinant = -12

Explanation:

rewrite the system as

-2 = 2x - 3y + 0z

0 = 0x + y - 2z

1 = -3x + 2y - z

then the coefficient matrix is

{ [2, -3, 0]

[0, 1, -2]

[-3, 2, -1] }

to find determinant

{ [2, -3, 0] , 2, -3

[0, 1, -2] , 0, 1

[-3, 2, -1] }, -3, 2

determinant = 2*1*-1 + (-3 * -2 * -3) + (0*0*2) - 0 - (2*-2*2) - 0

determinant = -2 - 18 + 0 - 0 + 8 = -12