Question

if $\begin{bmatrix}x\\ y\\ z\end{bmatrix} = \frac{1}{40} \begin{bmatrix}5&10&-5\\ -5&-2&13\\ 10&-4&6\end{bmatrix}\begin{bmatrix}5\\ 0\\ 5\end{bmatrix}$, then the value of $x + y + z$ is

• A. $3$
• B. $0$
• C. $2$
• D. $1$

Answer 1

Answer: (A)

Given$\begin{bmatrix}x\\ y\\ z\end{bmatrix} = \frac{1}{40} \begin{bmatrix}5&10&-5\\ -5&-2&13\\ 10&-4&6\end{bmatrix}\begin{bmatrix}5\\ 0\\ 5\end{bmatrix}$
$= \frac{1}{40} \begin{bmatrix}25&+0&-25\\ -25&+0&+65\\ 50&+0&+30\end{bmatrix}= \frac{1}{40}\begin{bmatrix}0\\ 40\\ 80\end{bmatrix}= \begin{bmatrix}0\\ 1\\ 2\end{bmatrix}$
$\Rightarrow x = 0, y = 1, z = 2$
$\therefore x + y + z = 0 + 1 + 2 = 3$