Can someone help me to solve this linear system?
The question is : Determine $a$ such that the equation system below has unique solution. Also determine the solution for such $a$.
2x + y - az = 3
3x + 4y +2az = 1
x - y + z = 2
I have tried many times to find a way to solve it but I did not succeed?
Hint: A system has a unique solution if the determinant is non-zero.
$$\begin{vmatrix} 2 & 1 & -a \\ 3 & 4 & 2a \\ 1 & -1 & 1\end{vmatrix} \neq 0$$
Expand along the last column
$$-7(-a)-2a(-3)+5 \neq 0$$
I believe you can handle the rest?