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.