Given:
$A = \left[ \begin{array} { r r r } - 6 & - 10 & 7 \ - 2 & 4 & 3 \end{array} \right] , B = \left[ \begin{array} { r r r } - 1 & 7 & - 3 \ 1 & 2 & - 2 \end{array} \right] , c = - 4$ and $d = 2$, determine $c A + d B$.
A) $\left[ \begin{array} { r r r } 22 & - 3 & 4 \ 10 & 6 & 1 \end{array} \right]$
B) $\left[ \begin{array} { r r r } 26 & 26 & - 22 \ 6 & - 20 & - 8 \end{array} \right]$
C) $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ 10 & - 12 & - 16 \end{array} \right]$
D) $\left[ \begin{array} { r r r } 22 & 54 & - 34 \ - 1 & 6 & 1 \end{array} \right]$
E) not possible

Question

Quizplus · Accepted Answer

To find $cA + dB$, we multiply each matrix $A$ and $B$ by their respective scalars $c$ and $d$, and then add the resulting matrices. For $cA$, multiply each element of $A$ by $-4$, and for $dB$, multiply each element of $B$ by $2$. Then, add the corresponding elements of the resulting matrices. The correct calculation leads to the matrix in choice C.

Given And d=2d = 2d=2 , Determine cA+dBc A + d BcA+dB

Given And $d = 2$ , Determine $c A + d B$