Answer to Question #54561 in Linear Algebra for Akanimo

Question

Find z by the use of determinant:
3x-4y+2z+8=0
x+5y-3z+2=0
5x+3y-z+6=0

Answer 1

Find z by the use of determinant:
3x-4y+2z+8=0
x+5y-3z+2=0
5x+3y-z+6=0

Solution

According Cramer's rule

| 3 -4 2|
D = det| 1 5 -3|= 120
| 5 3 -1|

| 3 -4 -8|
Dz =det | 1 5 -2| = 24
| 5 3 -6|


z=Dz/D = 5