Let $A = \left[ \begin{array} { c c c }
0 & 1 & 2 \
- 3 & 5 & 6
\end{array} \right]$ , $B = \left[ \begin{array} { c c }
5 & 8 \
- 2 & 0 \
7 & - 2
\end{array} \right]$ , and $C = \left[ \begin{array} { c c }
10 & 5 \
2 & - 8 \
12 & 5
\end{array} \right]$ . Evaluate $\left( A ^ { T } + B \right) - C$ .
A) $\left[ \begin{array} { c c }
15 & 10 \
1 & - 3 \
21 & 9
\end{array} \right]$
B) $\left[ \begin{array} { c c }
- 5 & 0 \
- 3 & 13 \
- 3 & - 1
\end{array} \right]$
C) $\left[ \begin{array} { c c }
5 & 0 \
3 & - 13 \
3 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c }
- 5 & 0 \
- 3 & - 1 \
- 3 & 13
\end{array} \right]$
E) $\left[ \begin{array} { c c }
1 & - 3 \
15 & 10 \
21 & 9
\end{array} \right]$

Question

Let $A = \left[ \begin{array} { c c c } 
0 & 1 & 2 \
- 3 & 5 & 6
\end{array} \right]$ , $B = \left[ \begin{array} { c c } 
5 & 8 \
- 2 & 0 \
7 & - 2
\end{array} \right]$ , and $C = \left[ \begin{array} { c c } 
10 & 5 \
2 & - 8 \
12 & 5
\end{array} \right]$ . Evaluate $\left( A ^ { T } + B \right) - C$ .  
A) $\left[ \begin{array} { c c } 
15 & 10 \
1 & - 3 \
21 & 9
\end{array} \right]$
B) $\left[ \begin{array} { c c } 
- 5 & 0 \
- 3 & 13 \
- 3 & - 1
\end{array} \right]$
C) $\left[ \begin{array} { c c } 
5 & 0 \
3 & - 13 \
3 & 1
\end{array} \right]$
D) $\left[ \begin{array} { c c } 
- 5 & 0 \
- 3 & - 1 \
- 3 & 13
\end{array} \right]$
E) $\left[ \begin{array} { c c } 
1 & - 3 \
15 & 10 \
21 & 9
\end{array} \right]$

Quizplus · Accepted Answer

First, transpose matrix $A$ to get $A^T$, then add $A^T$ to $B$, and finally subtract $C$ from the result. The correct calculation leads to option B.

Let A=[012−356]A = \left[ \begin{array} { c c c } 0 & 1 & 2 \\- 3 & 5 & 6\end{array} \right]A=[0−3​15​26​]

Let $A = \left[ \begin{array} { c c c } 0 & 1 & 2 \\- 3 & 5 & 6\end{array} \right]$