Question

The trace and determinant of a 2 x 2 matrix are known to be -2 and -35 respectively. Its eigen values are

• A. $-30and-5$
• B. $-37and-1$
• C. $-7and5$
• D. $17.5and-2$

Answer 1

The correct option is C $-7and5$

Trace of matrix = sum of eigen values
$\therefore$ ${\lambda }_1+{\lambda }_2=-2$
Determinant of matrix= product of eigen values
$\therefore$ ${\lambda }_1{\lambda }_2=-35$
$\Rightarrow$ ${\lambda }_1(-2-{\lambda }_1)=-35$
$\Rightarrow$ ${\lambda }_1^2+2{\lambda }_1-35=0$
$\Rightarrow$$({\lambda }_1+7)({\lambda }_1-5)=0$
$\Rightarrow$ ${\lambda }_1=-7,5$
$\Rightarrow$ ${\lambda }_2=5,-7$
$\therefore$ Eigen values are $(-7,5)$