If A is a 3x3 matrix and $\displaystyle a_1+2a_2-a_3=0$, then A must be singular.

True since $\displaystyle \begin{bmatrix}

0\\

0\\

0

\end{bmatrix}$ and $\displaystyle \begin{bmatrix}

1\\

-2\\

-1

\end{bmatrix}$ are solutions to the equations Ax=b.