Question

What is the product?

Answer 1

`=\begin{pmatrix}6&18\end{pmatrix}`

Explanation:

`\begin{pmatrix}4&2\end{pmatrix}\begin{pmatrix}-2&5\\ 7&-1\end{pmatrix}`

We will multiply the row of the first matrix to the column of the second matrix

`\begin{pmatrix}4&2\end{pmatrix}\begin{pmatrix}-2\\ 7\end{pmatrix}=4\left(-2\right)+2\cdot \:7`

`\begin{pmatrix}4&2\end{pmatrix}\begin{pmatrix}5\\ -1\end{pmatrix}=4\cdot \:5+2\left(-1\right)`

`=\begin{pmatrix}4\left(-2\right)+2\cdot \:7&4\cdot \:5+2\left(-1\right)\end{pmatrix}`

Simplifying each term we get a matrix of 1 X 2 dimension

`=\begin{pmatrix}6&18\end{pmatrix}`