(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find all solutions of a for which the resulting linear system has (a) no solution, (b) a unique solution, (c) infinetly many solutions.

x+z=4

2x+y+3z=5

-3x-3y+(a^2-5a)=a-8

2. Relevant equations

...Row reduction

3. The attempt at a solution

I solved the augmented matrix and got z=a-5/[(a-2)(a-3)], then got x and y in terms of z. I solved the homogeneous and only got the trivial solution regardless of a's value. I'm thinking that the system has no solution when a=2 or a=3, and has a unique solution when a equals any other real number. Is this correct?

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# Homework Help: Linear Algebra Solution Set Question

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