Question

If $e\left[\begin{array}{cc}{e}^x& e^y\\ e^y& e^x\end{array}\right]=\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$, then the values of $x$ and $y$ are respectively

• A. -1,-1
• B. 1, 1
• C. 0, 1
• D. 1, 0
• E. 0, 0

Answer 1

Answer: (A)

Given, $\left[\begin{array}{cc}{e}^x& e^y\\ e^y& e^x\end{array}\right]]=[\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$
$\Rightarrow \left[\begin{array}{cc}{e}^{x+1}& e^{y+1}\\ e^{y+1}& e^{x+1}\end{array}\right]=\left[\begin{array}{cc}cc{e}^0& e^0\\ e^0& e^0\end{array}\right](\because e^0=1)$
On equating the corresponding elements, we get
$e^{x+1}=e^0$ and $e^y+1=e^0$
$\Rightarrow x+1=0$ and $y+1=0$
$\Rightarrow x=-1$ and $y=-1$