(adsbygoogle = window.adsbygoogle || []).push({}); 0. The problem statement, all variables and given/known data

For which values of "a" the following system of equations has a unique solution? Infinitly many solutions?

x-y+z=2

ax-y+z=2

2x-2y+(2-a)z=4a

1. The attempt at a solution

I've put the system of equations under an amplied matrix and I reduced it.

I finally got the 3x3 identity matrix with the corresponding vector solution : { (4-8a+a²)/(1-a) ; (3a-2)/(2a-1)*(-2+6a-4a²)/(1-a)² ; (-2+6a-4a²)/(1-a)² ) }

I don't know what to do from here.

I see that "a" cannot be equal to 1 in the vector solution, but it could be equal to 1 in the original system of equations. So I probably did at least one error. But still, say the result is what I got, what do I have to do to find out the values of "a" satisfying the conditions of the question?

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# Homework Help: Condition of a system of equations to have infinitly many solutions

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