Determinants Matrices Question 19
Question: Let A be an nth-order square matrix and B be its adjoint, then $ | AB+KI _{n} | $ is (where K is a scalar quantity)
Options:
A) $ {{(| A |+K)}^{n-2}} $
B) $ {{(| A |+K)}^{n}} $
C) $ {{(| A |+K)}^{n-1}} $
D) none of these
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] We have, AB = A(adj A) $ =| A |I _{n} $
$ \therefore AB+KI _{n}=| A |I _{n}+KI _{n}=(| A |+k)I _{n} $
$ \Rightarrow | AB+KI _{n} |=| (| A |+K)I _{n} | $
(
$ \therefore | \alpha I _{n} |={{\alpha }^{n}} $ ) $ ={{(| A |+K)}^{n}} $
BETA
