If $A = \left[ \begin{array} { c c c }
2 & 0 & - 1 \
8 & 7 & 5
\end{array} \right]$ , then find $3 A ^ { T }$ .
A) $\left[ \begin{array} { c c c }
\frac { 3 } { 2 } & 0 & - \frac { 1 } { 3 } \
\frac { 3 } { 8 } & \frac { 1 } { 2 } & \frac { 3 } { 5 }
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- 3 & 15 \
0 & 21 \
6 & 24
\end{array} \right]$
C) $\left[ \begin{array} { c c }
6 & 24 \
0 & 21 \
- 3 & 15
\end{array} \right]$
D) $\left[ \begin{array} { c c c }
\frac { 3 } { 2 } & 0 & - \frac { 1 } { 3 } \
\frac { 3 } { 8 } & \frac { 3 } { 7 } & \frac { 3 } { 5 }
\end{array} \right]$
E) $\left[ \begin{array} { c c }
24 & 6 \
21 & 0 \
15 & - 3
\end{array} \right]$

Question

If $A = \left[ \begin{array} { c c c } 
2 & 0 & - 1 \
8 & 7 & 5
\end{array} \right]$ , then find $3 A ^ { T }$ .  
A) $\left[ \begin{array} { c c c } 
\frac { 3 } { 2 } & 0 & - \frac { 1 } { 3 } \
\frac { 3 } { 8 } & \frac { 1 } { 2 } & \frac { 3 } { 5 }
\end{array} \right]$
B) $\left[ \begin{array} { c c } 
- 3 & 15 \
0 & 21 \
6 & 24
\end{array} \right]$
C) $\left[ \begin{array} { c c } 
6 & 24 \
0 & 21 \
- 3 & 15
\end{array} \right]$
D) $\left[ \begin{array} { c c c } 
\frac { 3 } { 2 } & 0 & - \frac { 1 } { 3 } \
\frac { 3 } { 8 } & \frac { 3 } { 7 } & \frac { 3 } { 5 }
\end{array} \right]$
E) $\left[ \begin{array} { c c } 
24 & 6 \
21 & 0 \
15 & - 3
\end{array} \right]$

Quizplus · Accepted Answer

First, find the transpose of $A$, $A^T$, which flips the matrix over its diagonal. Then, multiply each element by 3. The correct calculation leads to option C.

If A=[20−1875]A = \left[ \begin{array} { c c c } 2 & 0 & - 1 \\8 & 7 & 5\end{array} \right]A=[28​07​−15​]

If $A = \left[ \begin{array} { c c c } 2 & 0 & - 1 \\8 & 7 & 5\end{array} \right]$