## Show that the Given 2 by 2 Matrix is Singular

## Problem 655

Consider the matrix $M = \begin{bmatrix} 1 & 4 \\ 3 & 12 \end{bmatrix}$.

**(a)** Show that $M$ is singular.

**(b) ** Find a non-zero vector $\mathbf{v}$ such that $M \mathbf{v} = \mathbf{0}$, where $\mathbf{0}$ is the $2$-dimensional zero vector.