Question

Use the following matrices to evaluate the given expression.

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

A+B

Short answer

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

Step-by-step solution

Step 1. Given Information

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

Step 2. Calculation

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