Question

If $\left[\begin{array}{cc}x+y& 2x+z\\ x-y& 2z+w\end{array}\right]=\left[\begin{array}{cc}4& 7\\ 0& 10\end{array}\right]$ then the values of $x,y,z$ and $w$ respectively are

• A. $2,2,3,4$
• B. $2,3,1,2$
• C. $3,3,0,1$
• D. None of these

Answer 1

Answer: (A)

since $\left[\begin{array}{cc}x+y& 2x+z\\ x-y& 2z+w\end{array}\right]=\left[\begin{array}{cc}4& 7\\ 0& 10\end{array}\right]$
$\Rightarrow x+y=\mathrm{4.....}\left(i\right)$,
$x-y=\mathrm{0.....}\left(ii\right)$,
$2x+z=\mathrm{7....}\left(iii\right)$and
$2z+w=\mathrm{10.....}\left(iv\right)$
on solving these equations, we get
$x=2,y=2,z=3,w=4$