Matrix vector multiplication inside summation

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I have an equation in the following form: $\sum_j A\bf{x}_j$

Where, $A$ - is a matrix and

$\bf{x}_j$ is a vector.

Can I write this equation in the following form?

$A\sum_j \bf{x}_j$

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Yes you can. Matrix multiplication is linear; that is, $A(x_1 + x_2) = Ax_1 + Ax_2$ and $A(cx) = cAx$ where $c$ is a constant. Your desired expression is just an extension of the first property.