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..

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- Oct 11th 2008, 11:17 AMleungstaComposition of Linear Transformations
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.. - Oct 11th 2008, 12:44 PMwatchmath
In general if $\displaystyle C=(c_1 c_2 \cdots c_n) $

where c_i are vector columns then

$\displaystyle

C\begin{pmatrix} k_1\\k_2\\\vdots\\k_n\end{pmatrix}=k_1c_1+\cdots k_nc_n$

Try to use this fact!