Chapter 16.2, Problem 4WE

To determine

To write: the value of $e$ of the sum or difference.

Answer to Problem 4WE

The value of $e$ is 6.

Explanation of Solution

Given information:

  $\left[\begin{array}{cc}4& 0\\ 2& 1\end{array}\right]+\left[\begin{array}{cc}12& -4\\ 9& 3\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ and $\left[\begin{array}{cc}9& 0\\ -2& 7\end{array}\right]-\left[\begin{array}{cc}3& 7\\ 8& -5\end{array}\right]=\left[\begin{array}{cc}e& f\\ g& h\end{array}\right]$

Calculation: The dimensions of the given matrices are the same. Subtract the corresponding elements.

  $\begin{array}{c}\left[\begin{array}{cc}9& 0\\ -2& 7\end{array}\right]-\left[\begin{array}{cc}3& 7\\ 8& -5\end{array}\right]=\left[\begin{array}{cc}e& f\\ g& h\end{array}\right]\\ \left[\begin{array}{cc}9-3& 0-7\\ -2-8& 7-\left(-5\right)\end{array}\right]=\left[\begin{array}{cc}e& f\\ g& h\end{array}\right]\\ \left[\begin{array}{cc}6& -7\\ -10& 12\end{array}\right]=\left[\begin{array}{cc}e& f\\ g& h\end{array}\right]\end{array}$

As, dimensions are equals then corresponding elements of the matrices will be equal.

Therefore, $e=6$

So, the value of $e$ is 6.