Q. 7 - Precalculus Enhanced with Graphing Utilities

Question

use the given matrices to compute each

expression.

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

$2A+C$

Step-by-Step Solution

Answer

The evaluation of the expression would be

$2A+C=\left[\begin{array}{cc}6& 4\\ 1& -11\\ 5& 4\end{array}\right]$

Step 1. Given

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

Step 2. Calculation

$$\begin{gathered} 2A \\ =2\left[\begin{array}{cc}1& -1\\ 0& -4\\ 3& -2\end{array}\right] \\ =\left[\begin{array}{cc}2& -2\\ 0& -8\\ 6& -4\end{array}\right] \end{gathered}$$

Now

$$\begin{gathered} 2A+C=\left[\begin{array}{cc}2& -2\\ 0& -8\\ 6& -4\end{array}\right]+\left[\begin{array}{cc}4& 6\\ 1& -3\\ -1& 8\end{array}\right] \\ =\left[\begin{array}{cc}6& 4\\ 1& -11\\ 5& 4\end{array}\right] \end{gathered}$$