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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.

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- Mar 27th 2010, 04:19 AMGIPCLinear equations with a parameter
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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. - Mar 27th 2010, 05:32 AMSoroban
Hello, GIPC!

Here's a start . . .

Quote:

Find for which parameter we have zero solutions, single solution and infinite number of solutions.

of the system: .*determinant*

Factor from column 3: .

Evaluate: .

And we have: .

. . Hence: .

Can you take it from here?

- Mar 27th 2010, 08:08 AMGIPC
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? - Mar 28th 2010, 04:45 AMGIPC
bump

anyone? (Worried)

this problem is giving me fits. - Mar 28th 2010, 05:44 AMHallsofIvy
Are you not

**trying**anything yourself? For example, it shouldn't take long to see that you can reduce the second equation to . And, as long as , we must have for any value of z. And then .