# Finding the dimensions of matrices?

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