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"Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values.

ax

_{1}+2x

_{2}+4x

_{3}= 4

−2x

_{1}−x

_{2}−5x

_{3}= −1

−2x

_{1}−5x

_{2}−x

_{3}= −12"

I know the answer to this one as i got it wrong and the website told me what it was, but not how to get it. What I've been doing is putting it into a matrix (obviously) and then trying to get it into reduced row echelon form, and then trying to get the bottom row into either "0 0 0 I #" form (for infinite solutions), "0 0 0 I 0" (for no solution) and "0 0 1 I #" (for unique solution) where I just represents a line. But that isn't working so I'm clearly doing something wrong.

I can't use a calculator for this class or anything so please only solutions that can be done by hand Thank you very much.