Chapter 2.3, Problem 37E

To determine

To find: value for the given case by using the matrices $A,B,C,D,E$ and $F$ . Write impossible if the matrix does not exist.

Answer to Problem 37E

  $\left[\begin{array}{ccc}\begin{array}{l}12\\ -2\end{array}& \begin{array}{l}2\\ -8\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right]$

Explanation of Solution

Given information:

The given matrices are as follows:

  $\begin{array}{ccc}\begin{array}{l}A=\left[\begin{array}{cc}5& 7\\ -6& 1\end{array}\right]\\ B=\left[\begin{array}{cc}3& 5\\ -1& 8\end{array}\right]\end{array}& \begin{array}{l}C=\left[\begin{array}{ccc}\begin{array}{l}4\\ 5\\ 9\end{array}& \begin{array}{l}-2\\ 0\\ 0\end{array}& \begin{array}{l}3\\ -1\\ 1\end{array}\end{array}\right]\\ D=\left[\begin{array}{ccc}\begin{array}{l}0\\ -2\\ 4\end{array}& \begin{array}{l}1\\ 3\\ 4\end{array}& \begin{array}{l}2\\ 0\\ -2\end{array}\end{array}\right]\end{array}& \begin{array}{l}E=\left[\begin{array}{ccc}\begin{array}{l}8\\ 3\end{array}& \begin{array}{l}-4\\ 1\end{array}& \begin{array}{l}2\\ -5\end{array}\end{array}\right]\\ F=\left[\begin{array}{ccc}\begin{array}{l}-6\\ 1\end{array}& \begin{array}{l}-1\\ 4\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right]\end{array}\end{array}$

The given case is $5A$ .

Calculation:

Multiply the matrix $A$ by $5$ and solve $5A$ as follows:

  $\begin{array}{c}5A=5\left[\begin{array}{cc}5& 7\\ -6& 1\end{array}\right]\\ =\left[\begin{array}{cc}5\left(5\right)& 7\left(5\right)\\ -6\left(5\right)& 1\left(5\right)\end{array}\right]\\ =\left[\begin{array}{cc}\begin{array}{l}25\\ -30\end{array}& \begin{array}{l}35\\ 5\end{array}\end{array}\right]\end{array}$

Thus, the values of $5A$ is $\left[\begin{array}{cc}\begin{array}{l}25\\ -30\end{array}& \begin{array}{l}35\\ 5\end{array}\end{array}\right]$ .