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Evaluate [ 1 2 1 ] \( \begin{bmatrix} 2 \\ 4 \\ 2 \end{bmatrix}\)

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  • If A is an m-by-n matrix and B is an n-by-p matrix, then their matrix product AB is the m-by-p matrix whose entries are given by dot product of the corresponding row of A and the corresponding column of B: $\begin{bmatrix}AB\end{bmatrix}_{i,j} = A_{i,1}B_{1,j} + A_{i,2}B_{2,j} + A_{i,3}B_{3,j} ... A_{i,n}B_{n,j}$
$\begin{bmatrix}1 & 2& 1\end{bmatrix}\begin{bmatrix}2\\4\\2\end{bmatrix}$
$\Rightarrow 1(2)+2(4)+1(2)$
$\Rightarrow 2+8+2.$
$\Rightarrow 12.$
answered Apr 11, 2013 by sharmaaparna1

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