Question

Consider the following matrix $A=\left[\begin{array}{cc}2& 3\\ x& y\end{array}\right]$. If the eigen values of A are 4 an 8, then

• A. $x=4,y=10$
• B. $x=5,y=8$
• C. $x=-3,y=9$
• D. $x=-4,y=10$

Answer 1

The correct option is D $x=-4,y=10$

Let ${\lambda }_1=4$ & ${\lambda }_2=8$
So $\Sigma a_{ii}={\lambda }_1+{\lambda }_2$ & $|A|={\lambda }_1.{\lambda }_2$
$2+y=4+8$ & $2y-3x=\left(4\right)\left(8\right)$
$y=10$ & $x=-4$