Question

I need to know where to start and how to begin to even find the answer . This is one thing I’m struggling on for some reason.

Answer 1

Given the following matrices:

`\begin{gathered} A=\begin{bmatrix}{2} & {-5} \\ {1} & {0}\end{bmatrix} \\ \\ B=\begin{bmatrix}{-2} & {-5} \\ {1} & {0}\end{bmatrix} \end{gathered}`

Question 1:

`\begin{gathered} 2A+3A \\ \\ 2\begin{bmatrix}{2} & {-5} \\ {1} & {0}\end{bmatrix}+3\begin{bmatrix}{2} & {-5} \\ {1} & {0}\end{bmatrix} \\ \\ =\begin{bmatrix}{2*2} & {-5*2} \\ {1*2} & {0*2}\end{bmatrix}+\begin{bmatrix}{2*3} & {-5*3} \\ {1*3} & {0}*3\end{bmatrix} \\ \\ =\begin{bmatrix}{4} & {-10} \\ {2} & {0}\end{bmatrix}+\begin{bmatrix}{6} & {-15} \\ {3} & {0}\end{bmatrix} \\ \\ =\begin{bmatrix}{4+6} & {-10-15} \\ {2+3} & {0+0}\end{bmatrix} \\ \\ \therefore2A+3A=\begin{bmatrix}{10} & {-25} \\ {5} & {0}\end{bmatrix} \end{gathered}`

Question 2: