Let $T$ : $\mathbb{R}^n \rightarrow \mathbb{R}^m$ be a matrix transformation given by
$T(x) = Ax$ ,
where $A$ is an $m \times n$ real matrix. Assuming $\mathbb{R}^n $ and $\mathbb{R}^m$ are given their standard Euclidean norms, prove that $T$ is continuous.
Not really too sure how to go about proving this, in this situation could you use the fact that if a linear map $T:V \rightarrow W$, with $V$ and $W$ normed vector spaces, is continous at $0$ then $T$ is continous?