91Ó°ÊÓ

The value of \( - 2A\) can be calculated as follows:

\(\begin{aligned}{c} - 2A = - 2\left( {\begin{aligned}{*{20}{c}}2&0&{ - 1}\\4&{ - 5}&2\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}{ - 4}&0&2\\{ - 8}&{10}&{ - 4}\end{aligned}} \right)\end{aligned}\)

The value of \(B - 2A\) can be calculated as follows:

\(\begin{aligned}{c}B - 2A = \left( {\begin{aligned}{*{20}{c}}7&{ - 5}&1\\1&{ - 4}&{ - 3}\end{aligned}} \right) - 2\left( {\begin{aligned}{*{20}{c}}2&0&{ - 1}\\4&{ - 5}&2\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}7&{ - 5}&1\\1&{ - 4}&{ - 3}\end{aligned}} \right) - \left( {\begin{aligned}{*{20}{c}}4&0&{ - 2}\\8&{ - 10}&4\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}3&{ - 5}&3\\{ - 7}&6&{ - 7}\end{aligned}} \right)\end{aligned}\)

The order of matrix \(A\) is \(2 \times 3\), and the order of matrix \(C\) is \(2 \times 2\). The number of column of \(A\) does not match with the number of rows of \(C\). Therefore, the matrix \(AC\) is not defined.

The product \(CD\) can be calculated as follows:

\(\begin{aligned}{c}CD = \left( {\begin{aligned}{*{20}{c}}1&2\\{ - 2}&1\end{aligned}} \right) \times \left( {\begin{aligned}{*{20}{c}}3&5\\{ - 1}&4\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}{1 \times 3 + 2 \times \left( { - 1} \right)}&{1 \times 5 + 2 \times 4}\\{\left( { - 2} \right) \times 3 + 1 \times \left( { - 1} \right)}&{\left( { - 2} \right) \times 5 + 1 \times 4}\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}{3 - 2}&{5 + 8}\\{ - 6 - 1}&{ - 10 + 4}\end{aligned}} \right)\\ = \left( {\begin{aligned}{*{20}{c}}1&{13}\\{ - 7}&{ - 6}\end{aligned}} \right)\end{aligned}\)

So, \( - 2A = \left( {\begin{aligned}{*{20}{c}}{ - 4}&0&2\\{ - 8}&{10}&{ - 4}\end{aligned}} \right)\), \(B - 2A = \left( {\begin{aligned}{*{20}{c}}3&{ - 5}&3\\{ - 7}&6&{ - 7}\end{aligned}} \right)\), \(AC\) is not defined and \(CD = \left( {\begin{aligned}{*{20}{c}}1&{13}\\{ - 7}&{ - 6}\end{aligned}} \right)\).