Problem: Let T: $\mathbb{R}^3\rightarrow\mathbb{R}^3$ be a linear map given by
$T\left[ \begin{matrix} x\\y\\ z\end{matrix} \right]= \left[ \begin{matrix} 3x-y\\z-x\\z-y\\\end{matrix} \right]$
- Find the Matrix representation of T with respect to the canonical basis of $\mathbb{R}^3$, and call it A.
I am not sure how this works. So the cananical basis of $\mathbb{R}^3$ is ${(1,0,0),(0,1,0),(0,0,1)}$ But I am unsure how to get a matrix represenation from a linear operator. Any help is appreciated.