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)

$3$

Answer 2

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