Checking Linearity For the mapping defined in each of Problems 1-16, determine whether $a$ not it is a linear transformation.
$T: \mathbb{R}^n \rightarrow \mathbb{R}^m, T(\overrightarrow{\mathbf{x}})=\mathbf{A} \overrightarrow{\mathbf{x}}$, where $\mathbf{A}$ is an $m \times n$ matrix