Determinants Matrices Question 95
If A and B be two square matrices of order $ n $ whose all the elements are essentially positive integers then the minimum value of $ tr\text{ (}AB^{2}) $ is equal to
Options:
A) $ {{\lambda }^{3}} $
B) $ {{\lambda }^{2}} $
C) $ 2{{\lambda }^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ tr(A)=\sum\limits _{i=1}^{n}a _{ii}\ge \lambda \sum\limits _{i=1}^{\lambda }a _{ii}\ge \lambda \sum\limits _{i=1}^{\lambda }a _{ij}\ge 1i,j} $ and $ tr(MN^{2})\neq{tr(M)}{{{tr(N)}}^{2}} $
BETA
