Question

One of the eigen value for the following matrix is

$\left[\begin{array}{cc}x& 2\\ 8& x\end{array}\right]$

• A. x - 4
• B. - x - 4
• C. 4
• D. -4

Answer 1

The correct option is A x - 4

$A=\left[\begin{array}{cc}x& 2\\ 8& x\end{array}\right]$

$|A-\lambda I|=0,\left[\begin{array}{cc}x-\lambda & 2\\ 8& x-\lambda \end{array}\right]=0$

$\Rightarrow (x-\lambda {)}^2-16=0$

$\Rightarrow (x-\lambda {)}^2=16$

$\Rightarrow x-\lambda =\pm 4$

So, ${\lambda }_1=x-4$

and ${\lambda }_2=x+4$

Hnece, the eigen value are x - 4 and x + 4