Question

Consider a 2 x 2 square matrix A = $\left[\begin{array}{cc}\sigma & X\\ \omega & \sigma \end{array}\right]$

Where x is unknown. If the eigen values of the matrix A are ($\sigma +j\omega$) and ($\sigma -j\omega$), then x is equal to

• A. +j$\omega$
• B. -j$\omega$
• C. +$\omega$
• D. -$\omega$

Answer 1

The correct option is D -$\omega$

A = $\left[\begin{array}{cc}\sigma & x\\ \omega & \sigma \end{array}\right]$

$\Rightarrow$ det [A] = ${\sigma }^2-\omega x$

$\because$ Eigen values of matrix A are ($\sigma +j\omega$) and ($\sigma -j\omega$) so ${\lambda }_1.{\lambda }_2$ = |A|

$\Rightarrow$ ${\sigma }^2+{\omega }^2$ = ${\sigma }^2-\omega x$

$\Rightarrow$ ${\omega }^2=-\omega X$

$\Rightarrow$ $\omega =-x$

$\therefore$ x= -$\omega$