Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

Use the following matrices to evaluate the given expression.

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

$2A+4B$

Step-by-Step Solution

Answer

$2A+4B=\left[\begin{array}{ccc}16& 10& -10\\ -6& 16& 4\end{array}\right]$

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

$$\begin{gathered} A=\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right], B=\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right] \\ 2A=2\left[\begin{array}{ccc}0& 3& -5\\ 1& 2& 6\end{array}\right] \\ =\left[\begin{array}{ccc}0& 6& -10\\ 2& 4& 12\end{array}\right] \\ 4B=4\left[\begin{array}{ccc}4& 1& 0\\ -2& 3& -2\end{array}\right] \\ =\left[\begin{array}{ccc}16& 4& 0\\ -8& 12& -8\end{array}\right] \\ 2A+4B=\left[\begin{array}{ccc}16& 10& -10\\ -6& 16& 4\end{array}\right] \end{gathered}$$