Solution
Given the following matrices:
[tex]\begin{gathered} A=\begin{bmatrix}{2} & {-5} \\ {1} & {0}\end{bmatrix} \\ \\ B=\begin{bmatrix}{-2} & {-5} \\ {1} & {0}\end{bmatrix} \end{gathered}[/tex]
Question 1:
[tex]\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\times2} & {-5\times2} \\ {1\times2} & {0\times2}\end{bmatrix}+\begin{bmatrix}{2\times3} & {-5\times3} \\ {1\times3} & {0}\times3\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}[/tex]
Question 2:
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