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Suppose you have a matrix $A =\begin{bmatrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{bmatrix}$ and $B = [1,2]$. I want to multiply the matrices together so I get a $3 \times 1$ resulting matrix where each entry is equal to $1*a1 + 2*a2$. How would I do this? The number of columns in matrix in matrix A is not the same as the number of rows in matrix B so I am not sure what to do.

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    $\begingroup$ You sure ly want $B$ to be a column, not a row, vector. $\endgroup$ – Julien Apr 19 '13 at 21:22
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If $A$ is a $m\times n$ and $B$ is a $j\times k$ matrix, then multiplication $AB$ is only defined when $n=j$, and the result will be an $m\times k$ matrix.

You could modify the example you have by transposing one of the matrices. For example, $AB^T$ is defined, and $BA^T$ is defined. The former would be a $3\times 1$ and the latter would be a $1\times 3$.

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