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4 votes
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

2 Answers

3 votes
I'm pretty sure it's no solution
User Sinwav
by
8.7k points
3 votes
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.


User DilTeam
by
8.4k points
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