Question

If 3, – 2 are the Eigen values of non-singular matrix A and

|A| = 4 . Then Eigen values of adj(1) are

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

Answer 1

Answer: (B)

4/3, –2

Answer 2

Since $A^{- 1} = \frac{adjA}{|A|}$and if $\lambda$is Eigen value of A then $\lambda^{- 1}$is Eigen value of $A^{- 1}$, thus for $adj(A)x = (A^{- 1}x)|A| = |A|.\lambda^{- 1}I$

$adj(A)$ corresponding to Eigen value

$\lambda = 3$ is = 4/3 and for $\lambda = - 2$is = $4/ - 2$ = –2