Question

If the sum of the matrices $\left[\begin{array}{c}x\\ x\\ y\end{array}\right],\left[\begin{array}{c}y\\ y\\ z\end{array}\right]$ and $\left[\begin{array}{c}z\\ 0\\ 0\end{array}\right]$ is the matrix $\left[\begin{array}{c}10\\ 5\\ 5\end{array}\right]$, then what is the value of $y$?

• A. $-5$
• B. $0$
• C. $5$
• D. $10$

Answer 1

Answer: (B)

$0$

Since, we have

$\left[\begin{array}{c}x\\ x\\ y\end{array}\right]+\left[\begin{array}{c}y\\ y\\ z\end{array}\right]+\left[\begin{array}{c}z\\ 0\\ 0\end{array}\right]=\left[\begin{array}{c}10\\ 5\\ 5\end{array}\right]$

$\therefore x+y+z=10,$ $x+y=5$ and $y+z=5$

Replacing $x+y=5$ in $x+y+z=10$
We have, $z=5$
Also, $y+z=5$
$\therefore y=5-z=0$
Option B is correct.