Question

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

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

Answer 1

Answer: (B)

Given, $ \left[ \begin{matrix} 4 & x-z \\ 2+y & xz \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 3 \\ -1 & 10 \\ \end{matrix} \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 $