Question

If $U=\left[\begin{array}{ccc}2& -3& 4\end{array}\right],X=\left[\begin{array}{ccc}0& 2& 3\end{array}\right],V=\left[\begin{array}{c}3\\ 2\\ 1\end{array}\right],Y=\left[\begin{array}{c}2\\ 2\\ 4\end{array}\right]$, then $UV+XY=$

• A. $\left[20\right]$
• B. $20$
• C. $\left[-20\right]$
• D. $-20$

Answer 1

The correct option is A

$\left[20\right]$

Explanation for the correct option:

To find the value of $UV+XY$ :

Given,

$U=\left[\begin{array}{ccc}2& -3& 4\end{array}\right],X=\left[\begin{array}{ccc}0& 2& 3\end{array}\right],V=\left[\begin{array}{c}3\\ 2\\ 1\end{array}\right],Y=\left[\begin{array}{c}2\\ 2\\ 4\end{array}\right]$

Then,

$\begin{array}{rcl}UV+XY& =& \left[2-34\right]\left[\begin{array}{c}3\\ 2\\ 1\end{array}\right]+\left[023\right]\left[\begin{array}{c}2\\ 2\\ 4\end{array}\right]\\ UV+XY& =& \left[6-6+4\right]+\left[0+4+12\right]\\ & =& \left[4\right]+\left[16\right]\\ & =& \left[20\right]\end{array}$

Hence, the correct option is A.