Question

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

Answer 1

Answer:

Determinant = -12

Step-by-step 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