Chapter EP, Problem 4.2.3EP

To determine

The performance of indicated matrix operation.

Answer to Problem 4.2.3EP

  $\left[\begin{array}{cc}0& 38\\ 45& 20\end{array}\begin{array}{c}-\text{18 }\\ 15\end{array}\right]$ .

Explanation of Solution

Given information:

Perform the indicated matrix operations. If the matrix does not exist, write impossible.

  $\left[\begin{array}{cc}45& 36\\ 63& 29\end{array}\begin{array}{c}\text{ 18 }\\ 5\end{array}\right]-\left[\begin{array}{cc}45& -2\\ 18& 9\end{array}\begin{array}{c}\text{ 36 }\\ -10\end{array}\right]$

Calculation:

The given matrix:

  $\left[\begin{array}{cc}45& 36\\ 63& 29\end{array}\begin{array}{c}\text{ 18 }\\ 5\end{array}\right]-\left[\begin{array}{cc}45& -2\\ 18& 9\end{array}\begin{array}{c}\text{ 36 }\\ -10\end{array}\right]$

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

  $\begin{array}{l}\left[\begin{array}{cc}45& 36\\ 63& 29\end{array}\begin{array}{c}\text{ 18 }\\ 5\end{array}\right]-\left[\begin{array}{cc}45& -2\\ 18& 9\end{array}\begin{array}{c}\text{ 36 }\\ -10\end{array}\right]\text{ [The given matrices]}\\ \left[\begin{array}{cc}45-45& 36-(-2)\\ 63-18& 29-9\end{array}\begin{array}{c}\text{ 18}-\text{36 }\\ 5-(-10)\end{array}\right]\text{ [Subtraction of two matrices]}\\ \left[\begin{array}{cc}0& 38\\ 45& 20\end{array}\begin{array}{c}-\text{18 }\\ 15\end{array}\right]\end{array}$

Therefore, the solution is $\left[\begin{array}{cc}0& 38\\ 45& 20\end{array}\begin{array}{c}-\text{18 }\\ 15\end{array}\right]$ .