Paper 4: Fundamentals of Business Mathematics & Statistic

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

 − − 

= =

 

 − 