MADE EASY TEST SERIES

Question

If 2, – 4 are the eigen values of a non­singular matrix A and |A| = ­8, then the
eigen values of Adj A are x and –y then the value of x + y is _________.
My doubt is x+y = 6 is possible or not ? ans is -6 given by ME.

Answer 1

Yup both are possible.

if x is eigen value of A then |A|/x is eigen value of Adj A

so eigen values for Adj A can be 8/2 and 8/(-4) i.e. 4 and -2

Case I)

suppose x = 4 and -y = -2  i.e y=2 then,

x+y=6

case II)

suppose x = -2 and -y = 4 i.e y= -4 then,

x+y = -2 + -4 =-6

Answer 2

sorry for the camera quality