Chapter 16.4, Problem 4ST

To determine

To find: $A-B$

Answer to Problem 4ST

  $A-B=\left[\begin{array}{cc}2& 2\\ -1& 3\end{array}\right]$

Explanation of Solution

Given information:

Let $A=\left[\begin{array}{cc}1& 4\\ 0& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& 2\\ 1& 0\end{array}\right]$

Calculation:

Substitute $A=\left[\begin{array}{cc}1& 4\\ 0& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& 2\\ 1& 0\end{array}\right]$

  $A-B=\left[\begin{array}{cc}1& 4\\ 0& 3\end{array}\right]-\left[\begin{array}{cc}-1& 2\\ 1& 0\end{array}\right]$

Now, simplify

  $\begin{array}{c}A-B=\left[\begin{array}{cc}1& 4\\ 0& 3\end{array}\right]-\left[\begin{array}{cc}-1& 2\\ 1& 0\end{array}\right]\\ =\left[\begin{array}{cc}1-\left(-1\right)& 4-2\\ 0-1& 3-0\end{array}\right]\\ =\left[\begin{array}{cc}2& 2\\ -1& 3\end{array}\right]\end{array}$

Therefore, $A-B=\left[\begin{array}{cc}2& 2\\ -1& 3\end{array}\right]$ .