Determinants Matrices Question 170
If $ A_1,A_3,…….,{A _{2n-1}} $ are n skew-symmetric matrices of same order, then $ B=\sum\limits _{r=1}^{n}{(2r-1){{({A _{2r-1}})}^{2}}} $ will be
Options:
A) Symmetric
B) Skew-symmetric
C) Neither symmetric nor skew-symmetric
D) Data is adequate
Show Answer
Answer:
Correct Answer: B
Solution:
- [b] $ B=A_1+3A_3^{3}+…..(2n-1){{({A _{2n-1}})}^{2n-1}} $
$ B^{T}=-[A_1+3A_3^{3}+….(2n-1){{({A _{2r-1}})}^{2r-1}}] $
$ = -B^T$ , so skew-symmetric
BETA
