Question

Hello I need help with this , I was studying and I can’t get this

Answer 1

Explanation

We are given the following:

We are required to determine if the equation in the image above holds true.

This can be achieved thus:

`\begin{gathered} Let\text{ }A=\begin{bmatrix}{5} & {8} \\ {1} & {3}\end{bmatrix},\text{ }B=\begin{bmatrix}{-4} & {2} \\ {7} & {9}\end{bmatrix},\text{ }C=\begin{bmatrix}{12} & {31} \\ {23} & {50}\end{bmatrix} \\ \\ \text{ Therefore, the equation becomes:} \\ A(B+C)=AB+AC \end{gathered}`

We know that the distribution property of matrices states:

Hence, the answer is:

`\text{ Yes. This shows the distributive property.}`

The correct option is D.