Determinants Matrices Question 74
Question: If $ |{A _{n\times n}}|=3 $ and $ |adjA|=243, $ what is the value of n ?
Options:
A) $ 4 $
B) $ 5 $
C) $ 6 $
D) $ 7 $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] As given: $ | {A _{n\times n}} |=3 $ and $ | adjA |=243 $ Determinant of adjoint A 13 given by: $ | adjA |={{| {A _{n\times n}} |}^{n-1}} $
$ \Rightarrow 243={3^{n-1}}\Rightarrow 3^{5}={3^{n-1}}\Rightarrow n-1=5 $
$ \Rightarrow n=6 $
BETA
