I'm asked to prove that if
$T:\mathbb{R}^m \rightarrow \mathbb{R}^n$
is a linear transformation, there exists a number $M$ such that
$\|T(h)\|\le M\|h\|$ for $h\in \mathbb{R}^m$.
I'm not sure whether I'm being asked to show that such a number (that is independent of $h$) exists or to show that such a $M$ exists for each $h$. Can someone please clarify?