Chapter EP, Problem 4.2.8EP

To determine

The solution of the matrix operation.

Answer to Problem 4.2.8EP

  $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$ .

Explanation of Solution

Given information:

Use matrices $A,B,C,D,$ and $E$ to find the following.

  $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right],C=\left[\begin{array}{cc}2& -2\\ -3& 3\end{array}\right],D=\left[\begin{array}{cc}-2& 2\\ 3& -3\end{array}\right],E=\left[\begin{array}{cc}5& -3\\ -2& 4\end{array}\right]$

Find $C+D$ .

Calculation:

The given matrix:

  $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],B=\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right],C=\left[\begin{array}{cc}2& -2\\ -3& 3\end{array}\right],D=\left[\begin{array}{cc}-2& 2\\ 3& -3\end{array}\right],E=\left[\begin{array}{cc}5& -3\\ -2& 4\end{array}\right]$

To add or subtract the two matrices with the same dimensions, add or subtract their corresponding elements are as shown below:

Find the matrix operation $C+D$ :

  $\begin{array}{l}C=\left[\begin{array}{cc}2& -2\\ -3& 3\end{array}\right],D=\left[\begin{array}{cc}-2& 2\\ 3& -3\end{array}\right]\text{ [The given matrix]}\\ \text{ C + D}\\ \left[\begin{array}{cc}2& -2\\ -3& 3\end{array}\right]+\left[\begin{array}{cc}-2& 2\\ 3& -3\end{array}\right]\text{ [Addition of the two matrix]}\\ =\left[\begin{array}{cc}2+(-2)& -2+2\\ -3+3& 3+(-3)\end{array}\right]\\ =\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\end{array}$

Thus, the solution is $\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$ .