Chapter 16.2, Problem 13OE

To determine

To simplify: the given expression.

Answer to Problem 13OE

The sum is $\left[\begin{array}{cc}11& 3\\ -6& 4\\ 6& 17\end{array}\right]$ .

Explanation of Solution

Given information:

Given expression,

  $2\left[\begin{array}{cc}5& -2\\ -3& 4\\ 0& 6\end{array}\right]+\left[\begin{array}{cc}1& 7\\ 0& -4\\ 6& 5\end{array}\right]$

Calculation: Consider the givn expression,

  $2\left[\begin{array}{cc}5& -2\\ -3& 4\\ 0& 6\end{array}\right]+\left[\begin{array}{cc}1& 7\\ 0& -4\\ 6& 5\end{array}\right]$

Now, solve the expression as shown,

  $\begin{array}{c}2\left[\begin{array}{cc}5& -2\\ -3& 4\\ 0& 6\end{array}\right]+\left[\begin{array}{cc}1& 7\\ 0& -4\\ 6& 5\end{array}\right]=\left[\begin{array}{cc}2\cdot 5& 2\cdot \left(-2\right)\\ 2\cdot \left(-3\right)& 2\cdot 4\\ 2\cdot 0& 2\cdot 6\end{array}\right]+\left[\begin{array}{cc}1& 7\\ 0& -4\\ 6& 5\end{array}\right]\\ =\left[\begin{array}{cc}10& -4\\ -6& 8\\ 0& 12\end{array}\right]+\left[\begin{array}{cc}1& 7\\ 0& -4\\ 6& 5\end{array}\right]\\ =\left[\begin{array}{cc}10+1& -4+7\\ -6+0& 8+\left(-4\right)\\ 0+6& 12+5\end{array}\right]\\ =\left[\begin{array}{cc}11& 3\\ -6& 4\\ 6& 17\end{array}\right]\end{array}$

Hence the sum is $\left[\begin{array}{cc}11& 3\\ -6& 4\\ 6& 17\end{array}\right]$ .