Question

If 3, -2 are the Exigent values of non-singular matrix A and |A|=4. Then Exigent values of Adj(A) are

• A. 3/4, -1/2
• B. 4/3, -2
• C. 12, -8
• D. -12, 8

Answer 1

The correct option is B 4/3, -2

$\begin{array}{c}{\lambda }_1=3,{\lambda }_2=-2\\ \left|A\right|=4\\ adj\left(A\right)=\left(A\right)\cdot A^{-1}\\ Ax=\lambda x\\ \frac{1}{\lambda }x=A^{-1}x\\ \left(\lambda I\cdot A^{-1}\right)=\frac{\left(A\right)\cdot \left(\lambda I-A^{-1}\right)}{\left(A\right)}\\ exigentvalueofadj\left(A\right)is\frac{\left(A\right)}{exigentvalueofA}\\ =\frac{4}{3},\frac{4}{-8}\\ =\left(\frac{4}{3},-2\right)\\ Hence,optionBiscorrectanswer.\end{array}$