Let $A = \left[ \begin{array} { c c c }
0 & \frac { 1 } { 2 } & - \frac { 2 } { 3 } \
- 1 & 2 & \frac { 1 } { 3 }
\end{array} \right]$ and $B = \left[ \begin{array} { c c c }
- 2 & 6 & 0 \
2 & \frac { 1 } { 2 } & - 1
\end{array} \right]$ . Evaluate $3 A - 4 B$ .
A) $\left[ \begin{array} { c c c }
8 & - 22 \frac { 1 } { 2 } & - 2 \
- 11 & 4 & 5
\end{array} \right]$
B) $\left[ \begin{array} { c c c }
- 8 & 22 \frac { 1 } { 2 } & 2 \
11 & - 4 & - 5
\end{array} \right]$
C) $\left[ \begin{array} { c c c }
- 8 & 25 \frac { 1 } { 2 } & - 2 \
5 & 8 & - 3
\end{array} \right]$
D) $\left[ \begin{array} { c c c }
8 & - 25 \frac { 1 } { 2 } & 2 \
- 5 & - 8 & 3
\end{array} \right]$
E) $\left[ \begin{array} { c c c }
8 & - 22 \frac { 1 } { 2 } & - 2 \
- 11 & - 4 & 5
\end{array} \right]$

Question

Let $A = \left[ \begin{array} { c c c } 
0 & \frac { 1 } { 2 } & - \frac { 2 } { 3 } \
- 1 & 2 & \frac { 1 } { 3 }
\end{array} \right]$ and $B = \left[ \begin{array} { c c c } 
- 2 & 6 & 0 \
2 & \frac { 1 } { 2 } & - 1
\end{array} \right]$ . Evaluate $3 A - 4 B$ .  
A) $\left[ \begin{array} { c c c } 
8 & - 22 \frac { 1 } { 2 } & - 2 \
- 11 & 4 & 5
\end{array} \right]$
B) $\left[ \begin{array} { c c c } 
- 8 & 22 \frac { 1 } { 2 } & 2 \
11 & - 4 & - 5
\end{array} \right]$
C) $\left[ \begin{array} { c c c } 
- 8 & 25 \frac { 1 } { 2 } & - 2 \
5 & 8 & - 3
\end{array} \right]$
D) $\left[ \begin{array} { c c c } 
8 & - 25 \frac { 1 } { 2 } & 2 \
- 5 & - 8 & 3
\end{array} \right]$
E) $\left[ \begin{array} { c c c } 
8 & - 22 \frac { 1 } { 2 } & - 2 \
- 11 & - 4 & 5
\end{array} \right]$

Quizplus · Accepted Answer

To find $3A - 4B$, multiply each element of matrix $A$ by 3 and each element of matrix $B$ by 4, then subtract the corresponding elements. The calculation yields the matrix given in option A.

Let A=[012−23−1213]A = \left[ \begin{array} { c c c } 0 & \frac { 1 } { 2 } & - \frac { 2 } { 3 } \\- 1 & 2 & \frac { 1 } { 3 }\end{array} \right]A=[0−1​21​2​−32​31​​]

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