Chapter 16.2, Problem 15WE

To determine

To simplify: the given expression.

Answer to Problem 15WE

The difference is $\left[\begin{array}{cc}-37& 8\\ -3& -20\\ 28& -3\end{array}\right]$ .

Explanation of Solution

Given information:

Given expression,

  $\left[\begin{array}{cc}3& 0\\ 5& -4\\ 0& -3\end{array}\right]-4\left[\begin{array}{cc}10& -2\\ 2& 4\\ -7& 0\end{array}\right]$

Calculation: Consider the givn expression,

  $\left[\begin{array}{cc}3& 0\\ 5& -4\\ 0& -3\end{array}\right]-4\left[\begin{array}{cc}10& -2\\ 2& 4\\ -7& 0\end{array}\right]$

Now, subtract the expression as shown,

  $\begin{array}{c}\left[\begin{array}{cc}3& 0\\ 5& -4\\ 0& -3\end{array}\right]-4\left[\begin{array}{cc}10& -2\\ 2& 4\\ -7& 0\end{array}\right]=\left[\begin{array}{cc}3& 0\\ 5& -4\\ 0& -3\end{array}\right]-\left[\begin{array}{cc}4\cdot 10& 4\cdot \left(-2\right)\\ 4\cdot 2& 4\cdot 4\\ 4\cdot \left(-7\right)& 4\cdot 0\end{array}\right]\\ =\left[\begin{array}{cc}3& 0\\ 5& -4\\ 0& -3\end{array}\right]-\left[\begin{array}{cc}40& -8\\ 8& 16\\ -28& 0\end{array}\right]\\ =\left[\begin{array}{cc}3-40& 0-\left(-8\right)\\ 5-8& -4-16\\ 0-\left(-28\right)& -3-0\end{array}\right]\\ =\left[\begin{array}{cc}-37& 8\\ -3& -20\\ 28& -3\end{array}\right]\end{array}$

Hence the difference is $\left[\begin{array}{cc}-37& 8\\ -3& -20\\ 28& -3\end{array}\right]$ .