Chapter 16.2, Problem 19WE

To determine

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

Answer to Problem 19WE

The value of $a$ is 16.

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. Add the corresponding elements.

  $\begin{array}{c}\left[\begin{array}{cc}4& 0\\ 2& 1\end{array}\right]+\left[\begin{array}{cc}12& -4\\ 9& 3\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\\ \left[\begin{array}{cc}4+12& 0+\left(-4\right)\\ 2+9& 1+3\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\\ \left[\begin{array}{cc}16& -4\\ 11& 4\end{array}\right]=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\end{array}$

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

Therefore, $a=16$

So, the value of $a$ is 16.