Chapter 2.3, Problem 10CFU

To determine

To find: value for the given case by using the matrices X , Y and Z . Write impossible if the matrix does not exist.

Answer to Problem 10CFU

  $\left[\begin{array}{cc}-5& 2\\ 2& -8\end{array}\right]$

Explanation of Solution

Given information:

The given matrices are as follows:

  $X=\left[\begin{array}{cc}4& 1\\ -2& 6\end{array}\right]Y=\left[\begin{array}{cc}0& -3\end{array}\right]\text{ Z}=\left[\begin{array}{cc}-1& 3\\ 0& -2\end{array}\right]$

The given case is $Z-X$ .

Calculation:

Solve $Z-X$ as follows:

  $\begin{array}{c}Z-X=\left[\begin{array}{cc}-1& 3\\ 0& -2\end{array}\right]-\left[\begin{array}{cc}4& 1\\ -2& 6\end{array}\right]\\ =\left[\begin{array}{cc}-5& 2\\ 2& -8\end{array}\right]\end{array}$

Thus, the values of $Z-X$ is $\left[\begin{array}{cc}-5& 2\\ 2& -8\end{array}\right]$ .