Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.63

B’

0 2 3

2 0 4

3 4 0

 

= − − 

 

− 

0 2 3

2 0 4 B

3 4 0

−

= −^

(^) − (^)
So B = A – A’ is skew symmetric matrix.
SELF EXAMINATION QUESTIONS
(1) Find A + A’ where

5 7 2

A 9 8 11

5 6 3

 

= − 

 

 − 

& Prove (A + A’) is symmetric.

(2) Find A – A’ where

11 7 9

A 8 6 5

6 2 13

 

= − 

 

 

& Prove (A – A’) is symmetric.

Example 108 : If =3x 0 +y x^0 −y    = 7 0 0 1
   
Then find x & y
Solution :
If two matrices are equal, then their corresponding elements are equal
3x + y = 7 (i)
x – y = 1 (ii)
Adding (i) & (ii)
4x = 8
x = 2
Put x in (i)
3(2) + y = 7
y = 7 - 6 = 1
(x = 2 & y = 1)

Example 109 :If 3x + y =

2 7

8 9

 

  

& 2x – y =

3 3

12 11

 

 

Then find x & y