let $\displaystyle B$ be an $\displaystyle n \times p$ matrix. For each $\displaystyle j \ (1 \leq j \leq p)$ let $\displaystyle v_j$ denote the jth column of B. Prove that:

$\displaystyle v_j =Be_j$, where $\displaystyle e_j$ is the jth standard vector of $\displaystyle F^p$

so far all I have is:

$\displaystyle v_j = \left( \begin{array}{c}

B_{1j} \\

B_{2j} \\

\vdots \\

B_{mj}

\end{array} \right) = Be_{j} \therefore v_j = Be_j $

is this correct?