How do I find for which K parameter we have zero solutions, single solution and infinite number of solutions? I can't seem to do it with the Gaussian Elimination.
Hello, GIPC!
Here's a start . . .
Consider the determinant of the system: .
Find for which parameter we have zero solutions, single solution and infinite number of solutions.
Factor from column 3: .
Evaluate: .
And we have: .
. . Hence: .
Can you take it from here?
I have another question, if the system changes to:
x + (k^2 -6)y + (4k+4)z = 5k+3
(3k^2 -3)y +(6k+6)z = 9k+6
for which k do i have a single solution, no solution and infinite solotions? How do I solve it?