Let $V$ a $F$-vectorial space with finite dimension, $T: V \rightarrow V$ lineal and $W$ invariant under $T$ with dimension $n$ Let $V$ a $F$-vectorial space with finite dimension, $T: V \rightarrow V$ lineal and $W$ a proper subspace nonzero of $V$ invariant under $T$ with dimension $n$.Then there exist a basis $\beta$ of $V$ such that: $[T]_{\beta}= \left[ {\begin{array}{cc} A & B \\\ 0 & C \\\ \end{array} } \right]$ I tried taking the canonical basis of V and get a transformation with this basis but i´m so confused with this exercise some help please.

Whenever you have such abstract looking questions especially in linear algebra, I find it best to look at concrete examples. Say, we have the following matrix-

$$\begin{pmatrix} * & *&0 \\\ * & * &0 \\\ 0 & 0 &1 \\\ \end{pmatrix}\begin{pmatrix}0\\\0\\\x\end{pmatrix}=\begin{pmatrix}0\\\0\\\x\end{pmatrix} $$ So the subspace spanned by $\begin{pmatrix}0\\\0\\\1\end{pmatrix}$ is invariant under this transformation. Now you can why the matrix should be of that form. Just a little hint to put things in perspective.