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I'm trying to figure out if this matrix operation is possible:

$$\begin{bmatrix}1&2\\3&7\end{bmatrix}\times\begin{bmatrix}1\\5\end{bmatrix}$$

I know that in order to do that I need to find the dimensions of each matrix. How would I do that? What are the dimensions?

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2 Answers 2

The dimension of each matrix is just how many numbers it has down and across, respectively. So your first matrix has dimension $2\times 2$ because it has the form $\pmatrix{*&*\\*&*}$ -- it doesn't matter what the four numbers in it is, just that they are arranged in this shape -- and the second matrix has dimension $2\times 1$ because it has the form $\pmatrix{*\\*}$.

Because the second dimension of the first matrix is the same as the first dimension of the second matrix, they can be multiplied.

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Yes. If the size of first factor is $m\times p$ and the second is $p\times n$, the size of the product is $m\times n$.

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