Question

6 6 4 1 5 -8 If A = 7. -4 4 and B = 9 -5 -8, find 3A + 9B. - 6 9 -3 9 -5 2 a. 57 69 12 51 39 60 90 -51 12 36 -21 60 -27 66 -21 -81 96 -33 b. d. 9 -27 84 27 63 -60 -60 33 84 102 -57 -60 -99 72 63 -27 -18 9

Answer 1

$3A\text{ + 9B = }\begin{bmatrix}{27} & {63} & {-60} \\ {102} & {-57} & {-60} \\ {63} & {-18} & {9}\end{bmatrix}\text{ option D}$

Explanation:

$\begin{gathered} \begin{bmatrix}{6} & {6} & {4} \\ {7} & {-4} & {4} \\ {-6} & {9} & {-3}\end{bmatrix}=\text{ A} \\ \begin{bmatrix}{1} & {5} & {-8} \\ {9} & {-5} & {-8} \\ {9} & {-5} & {2}\end{bmatrix}=\text{ B} \end{gathered}$

3A + 9B = multiply 3 by matrix A and multiply 9 by matrix B. Then sum them together.

$\begin{gathered} 3\begin{bmatrix}{6} & {6} & {4} \\ {7} & {-4} & {4} \\ {-6} & {9} & {-3}\end{bmatrix}=\text{ }\begin{bmatrix}{18} & {18} & {12} \\ {21} & {-12} & {12} \\ {-18} & {27} & {-9}\end{bmatrix} \\ 9\begin{bmatrix}{1} & {5} & {-8} \\ {9} & {-5} & {-8} \\ {9} & {-5} & {2}\end{bmatrix}=\text{ }\begin{bmatrix}{9} & {45} & {-72} \\ {81} & {-45} & {-72} \\ {81} & {-45} & {18}\end{bmatrix} \end{gathered}$$\begin{gathered} 3A\text{ + 9B = }\begin{bmatrix}{18} & {18} & {12} \\ {21} & {-12} & {12} \\ {-18} & {27} & {-9}\end{bmatrix}+\text{ }\begin{bmatrix}{9} & {45} & {-72} \\ {81} & {-45} & {-72} \\ {81} & {-45} & {18}\end{bmatrix} \\ 3A\text{ + 9B = }\begin{bmatrix}{27} & {63} & {-60} \\ {102} & {-57} & {-60} \\ {63} & {-18} & {9}\end{bmatrix} \end{gathered}$

From the above, the answer is option D