Consider the system of linear equations

x − 3z = −3

−2x − Ay + z = 2

x + 2y + Az = 1

Find the respective values of A such that the system is inconsistent..

I've tried rewriting this as an augemented matrix, then doing row operations to get the bottom row as [0 0 {(A+3)/2 - 5/A} | 2-(4/A)]

so for it to be inconsistent i know that it has to look like [0 0 0 | K] for any real k

so (A+3)/2 - 5/A should equal zero, but 2-4A shouldn't because that would make the system have infinitely many solutions, not NO solutions.

but i can't find any values of A that solve both these equations!

Please help, I'm so confused