## Determine whether the Matrix is Nonsingular from the Given Relation

## Problem 698

Let $A$ and $B$ be $3\times 3$ matrices and let $C=A-2B$.

If

\[A\begin{bmatrix}

1 \\

3 \\

5

\end{bmatrix}=B\begin{bmatrix}

2 \\

6 \\

10

\end{bmatrix},\]
then is the matrix $C$ nonsingular? If so, prove it. Otherwise, explain why not.