Chapter 16, Problem 2CT

To determine

To find: The value of matrix $A+B$ .

Answer to Problem 2CT

The value of matrix $A+B=\left[\begin{array}{ccc}0& 2& 8\\ 5& -6& 2\\ 4& 2& -1\end{array}\right]$

Explanation of Solution

Given information:

The given expression is

  $A=\left[\begin{array}{ccc}2& 1& 3\\ 0& -1& 1\\ 4& -1& 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2& 1& 5\\ 5& -5& 1\\ 0& 3& -1\end{array}\right]$

Calculation:

Consider the expression

Let $A=\left[\begin{array}{ccc}2& 1& 3\\ 0& -1& 1\\ 4& -1& 0\end{array}\right]$ and $B=\left[\begin{array}{ccc}-2& 1& 5\\ 5& -5& 1\\ 0& 3& -1\end{array}\right]$

Calculate the expression.

  $\begin{array}{c}A+B=\left[\begin{array}{ccc}2& 1& 3\\ 0& -1& 1\\ 4& -1& 0\end{array}\right]+\left[\begin{array}{ccc}-2& 1& 5\\ 5& -5& 1\\ 0& 3& -1\end{array}\right]\\ =\left[\begin{array}{ccc}0& 2& 8\\ 5& -6& 2\\ 4& 2& -1\end{array}\right]\end{array}$

Therefore, the value of matrix is $A+B=\left[\begin{array}{ccc}0& 2& 8\\ 5& -6& 2\\ 4& 2& -1\end{array}\right]$ .