Discussion Forum



1)

 If A is non-singular matrix such that  (A-2l) (A-4l)= 0 , then A+8 A-1= 

 


A) l

B) 0

C) 3 l

D) 6 l

Answer:

Option D

Explanation:

 We have | A|≠ o

 $\Rightarrow$   A-1 is exists

 Since  , (A-2l) (A-4l)=0

$\Rightarrow$         A2- A(4l)-2l(A)+8l .l=0

$\Rightarrow$     A2-4 Al-2 Al+8l=0

$\Rightarrow$        A2-6 Al+8l=0

$\Rightarrow$     A2-6A+8l=0

 On pre multiply  both sides by A-1 , we get

                 A-1A2-6A-1 A+8A-1l=0

$\Rightarrow$    lA-6l+8A-1=0

$\Rightarrow$    A-6l+8 A-1 =0

$\Rightarrow$   A+8A-1  = 6l