2.62 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS
Algebra
SYMMETRIC MATRIX
Any matrix A is called to be symmetric matrix if A’ = A
Example
a b c
A^35 , A b d e
(^47) c e f
= =
SKEW SYMMETRIC MATRIX
Any matrix A is called to be skew symmetric if A’ = -A
Example
0 4 0 b c
A 4 0 , A b 0 c
c e 0
= = −
−
− −
Example 106 : Find A + A’ where
A^25
7 8
=
& Prove A + A’ is symmetric
Solution: (^) A+A '= 72 85 + 52 78
4 12
12 16
=
Let B=12 16^412
(∴B = A + A’)
B’=12 16^412
= B
So, B =A+A’, is symmetric matrix
Example 107 : Find A – A’ where
3 2 5
A 4 7 6
8 2 9
=
& Prove A – A’ is skew symmetric.
Solution:A – A’
3 2 5 3 4 8
4 7 6 2 7 2
8 2 9 5 6 9
=^ −^
(^)
0 2 3
2 0 4 B(say)
3 4 0