Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{A}=\left[\begin{array}{cc}2 \mathrm{x} & 0 \\ \mathrm{x} & \mathrm{x}\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]$, then what is the value of $\mathrm{x}$?
Options:
Solution:
1063 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{2}$
Given matrices are :
$\mathrm{A}=\left[\begin{array}{cc}2 \mathrm{x} & 0 \\ \mathrm{x} & \mathrm{x}\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]$
$\mathrm{AA}^{-1}=\mathrm{I}$
$\Rightarrow\left[\begin{array}{cc}2 \mathrm{x} & 0 \\ \mathrm{x} & \mathrm{x}\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}2 x & 0 \\ 0 & 2 x\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \Rightarrow 2 x=1$
$\mathrm{A}=\left[\begin{array}{cc}2 \mathrm{x} & 0 \\ \mathrm{x} & \mathrm{x}\end{array}\right]$ and $\mathrm{A}^{-1}=\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]$
$\mathrm{AA}^{-1}=\mathrm{I}$
$\Rightarrow\left[\begin{array}{cc}2 \mathrm{x} & 0 \\ \mathrm{x} & \mathrm{x}\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -1 & 2\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{cc}2 x & 0 \\ 0 & 2 x\end{array}\right]=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right] \Rightarrow 2 x=1$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.