Question

In Problems 13–16, use the following matrices to compute each expression.

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

$A+C$

Short answer

$A+C=\left[\begin{array}{cc}4& -4\\ 3& 9\\ 4& 4\end{array}\right]$

Step-by-step solution

Step 1. Given information

The given matrices are

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

Step 2. Find the value of expression A+C.

$$\begin{gathered} A+C \\ =\left[\begin{array}{cc}1& 0\\ 2& 4\\ -1& 2\end{array}\right]+\left[\begin{array}{cc}3& -4\\ 1& 5\\ 5& 2\end{array}\right] \\ =\left[\begin{array}{cc}4& -4\\ 3& 9\\ 4& 4\end{array}\right] \end{gathered}$$