Question

Which Matrix is equal to A-2B+C

Answer 1

It is convenient to use the matrix capability of your calculator to do this. The result is ...
$\left[ \begin{array}{cc}-1&4\\5&-7\end{array} \right]$

Answer 2

$\bf A= \begin{bmatrix} 5&2\\3&0 \end{bmatrix}\qquad B= \begin{bmatrix} 4&3\\-1&6 \end{bmatrix}\qquad C= \begin{bmatrix} 2&8\\0&5 \end{bmatrix}\\\\ -------------------------------\\\\ 2B\implies 2\begin{bmatrix} 4&3\\-1&6 \end{bmatrix}\implies \begin{bmatrix} 2\cdot 4&2\cdot 3\\2\cdot -1&2\cdot 6 \end{bmatrix}\implies \begin{bmatrix} 8&6\\-2&12 \end{bmatrix}$

$\bf \stackrel{A-2B}{\begin{bmatrix} 5&2\\3&0 \end{bmatrix}-\begin{bmatrix} 8&6\\-2&12 \end{bmatrix}}\implies \begin{bmatrix} -3&-4\\5&-12 \end{bmatrix} \\\\\\ \stackrel{A-2B+C}{\begin{bmatrix} -3&-4\\5&-12 \end{bmatrix}+\begin{bmatrix} 2&8\\0&5 \end{bmatrix}}\implies \begin{bmatrix} -1&4\\5&-7 \end{bmatrix}$