Question

Find the values of $x,y$ and $z$ from the following equations $\left[\begin{array}{cc}4& x-z\\ 2+y& xz\end{array}\right]=\left[\begin{array}{cc}4& 3\\ -1& 10\end{array}\right]$

• A. $x=-5,y=3,z=2$
• B. $x=5,y=-3,z=2$
• C. $x=5,y=3,z=-2$
• D. $x=5,y=-3,z=-2$

Answer 1

Answer: (B)

Given, $\left[\begin{array}{cc}4& x-z\\ 2+y& xz\end{array}\right]=\left[\begin{array}{cc}4& 3\\ -1& 10\end{array}\right]$
On comparing the corresponding elements, we get
$x-z=3$ ..(i)
$2+y=-1$
$\Rightarrow$ $y=-1-2=-3$ ..(ii)
and $xz=10$ ..(iii)
Now, ${(x+z)}^2={(x-z)}^2+4xz$
$={(3)}^2+4\times 10$
$=9+40$
$\Rightarrow$ ${(x+z)}^2=49$
$\Rightarrow$ $x+z=7$ ..(iv)
On adding Eq. (i) and (iv), we get
$2x=10$
$\Rightarrow$ $x=5$
From Eq. (i), we get $5-z=3$
$\Rightarrow$ $-z=3-5$
$\Rightarrow$ $z=2$
Hence, $x=5,y=-3,z=2$