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

The Correct Option is B

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