Composition of Linear Transformations

leungsta · #1 $Old$ October 11th, 2008, 01:17 PM

Let A be an m x n matrix and B be an n x p matrix. For each j let uj and vj denote the jth columns of AB and B, respectively.

Prove vj = Bej, where ej is the jth standard vector of F^p (j is a subscript)

Thanks..

watchmath · #2 $Old$ October 11th, 2008, 02:44 PM

In general if $C=(c_1 c_2 \cdots c_n)$
where c_i are vector columns then
$C\begin{pmatrix} k_1\\k_2\\\vdots\\k_n\end{pmatrix}=k_1c_1+\cdots k_nc_n$

Try to use this fact!