Question

When does a system of matrices have no solution, infinetly many solution, a unique solution.

9x+ky=9
kx+y=-3
find all the values of k such as the system has:
no solution
one unique solution
infinetly many solution

Answer 1

I'm pretty sure it's no solution

Answer 2

The system has infinitely many solutions or has no solutions when:

`(9)/(k) = (k)/(1) =(\\eq) (9)/(-3) , \\ k^2=9, \\ k=\pm 3`.

1. k=3, then
`9x+3y=9 \\ 3x+y=-3` has no solutions, because


`(9)/(3) = (3)/(1)\\eq (9)/(-3)`.

2. k=-3, then
`9x-3y=9 \\ -3x+y=-3` has infinetely many solutions, because

`(9)/(-3) = (-3)/(1)= (9)/(-3)`.

When
`k\\eq \pm3`, the system has unique solution.