Find k such that the system of equations has no unique solution.

Question

-2x -7y +1z=4
6x -5y -3z=14
kx -2y -z=5

 

k=?

 

I need help understanding how to solve this problem.

Answer 1

To ensure there is no unique solution, you need to make the principal determinant equal to zero.

 

|-2  -7  1|

| 6  -5 -3| = 0

| k  -2 -1|

 

Expand the determinant, set it equal to zero, and solve for k.