1. ## [SOLVED] Homogeneous system

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

True since $\begin{bmatrix}
0\\
0\\
0
\end{bmatrix}$
and $\begin{bmatrix}
1\\
-2\\
-1
\end{bmatrix}$
are solutions to the equations Ax=b.

2. true since, it has a nontrivial solution to the homogenous eqn.