Evaluate the expression.
$$\frac { 2 } { 9 } \left[ \begin{array} { l l l }
5 & - 2 & 1
\end{array} \right] + \left[ \begin{array} { l l l }
4 & 8 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$
B) $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$
C) $\left[ \begin{array} { l l l } \frac { 14 } { 9 } & \frac { 4 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$
D) $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$
E) not possible

Question

Evaluate the expression.
$$\frac { 2 } { 9 } \left[ \begin{array} { l l l } 
5 & - 2 & 1
\end{array} \right] + \left[ \begin{array} { l l l } 
4 & 8 & - 1
\end{array} \right]$$
A) $\left[ \begin{array} { l l l } 9 & 6 & 0 \end{array} \right]$
B) $\left[ \begin{array} { l l l } - \frac { 26 } { 9 } & - \frac { 76 } { 9 } & \frac { 11 } { 9 } \end{array} \right]$
C) $\left[ \begin{array} { l l l } \frac { 14 } { 9 } & \frac { 4 } { 9 } & \frac { 1 } { 9 } \end{array} \right]$
D) $\left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]$
E) not possible

Quizplus · Accepted Answer

First, we need to evaluate the expression inside the brackets:

$$\frac{2}{9}\left[\begin{array}{lll}5&-2&1\end{array}\right]=\left[\begin{array}{lll}\frac{10}{9}&-\frac{4}{9}&\frac{2}{9}\end{array}\right]$$

Then, we can simplify the entire expression by distributing the scalar $\frac{2}{9}$:

\begin{align*}
\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1 \end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1 \end{array} \right] &= \left[ \begin{array} { l l l } \frac { 20 } { 9 } & - \frac { 8 } { 9 } & \frac { 4 } { 9 } \end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1 \end{array} \right] \
&= \left[ \begin{array} { l l l } \frac { 20 } { 9 } + 4 & - \frac { 8 } { 9 } + 8 & \frac { 4 } { 9 } - 1 \end{array} \right] \
&= \left[ \begin{array} { l l l } \frac { 46 } { 9 } & \frac { 68 } { 9 } & - \frac { 7 } { 9 } \end{array} \right]
\end{align*}

Therefore, the answer is choice D.

Evaluate the Expression 29[5−21]+[48−1]\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]92​[5​−2​1​]+[4​8​−1​]

Evaluate the Expression $\frac { 2 } { 9 } \left[ \begin{array} { l l l } 5 & - 2 & 1\end{array} \right] + \left[ \begin{array} { l l l } 4 & 8 & - 1\end{array} \right]$