Linear system/Parameter/Size of solution/Exercise

We consider the linear system

${\begin{matrix}2x&-ay&&=&-2\\ax&&+3z&=&3\\-{\frac {1}{3}}x&+y&+z&=&2\end{matrix}}$

over the real numbers, depending on the parameter ${}a\in \mathbb {R}$.

For which ${}a$ does the system of equations have no solution, one solution or infinitely many solutions?

Create a solution