Question

If $\begin{bmatrix}e^{x}&e^{y}\\\ e^{y}&e^{x}\end{bmatrix} = \begin{bmatrix}1&1\\\ 1&1\end{bmatrix}$, then the values of $x$ and $y$ are respectively:

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

Answer 1

Answer: (B)

0, 0

Answer 2

Given, $\begin{bmatrix}e^{x} & e^{y} \\\ e^{y} & e^{x}\end{bmatrix}=\begin{bmatrix}1 & 1 \\\ 1 & 1\end{bmatrix}$
$\Rightarrow \begin{bmatrix}e^{x} & e^{y} \\\ e^{y} & e^{x}\end{bmatrix}=\begin{bmatrix}e^{0} & e^{0} \\\ e^{0} & e^{0}\end{bmatrix} (\because e^{0}=1)$
On equating the corresponding elements,
$e^{x}=e^{0}$ and $e^{y}=e^{0}$
$\Rightarrow x=0$ and $y=0$

So, the correct option is (B): 0, 0