Let $$T\colon V\to W$$ be a linear transformation defined by the matrix A where $$A= \left[ \begin{matrix} -1 & 2 & 3 \\ 0 & 1 & 0 \\ 1 & -1 & -2 \\ 0 & 0 & 1 \\ \end{matrix} \right] $$
I have to find basis for $V = R^3$ and $W = R^4$ to make the matrix of T as simple as possible.
How would I go about doing this? I've never done something like this before and I'm not sure where to start.