Paper 4: Fundamentals of Business Mathematics & Statistic

2.56 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

2.8 MATRICES AND DETERMINANTS

2.8.1. Matrix

A set of mn numbers arranged in the form of rectangular array of m rows and n columns is called an

(m X n) matrix (to be read as ‘m’ by’n’matrix)

An m x n matrix is usually written as

11 12 13 1n

12 22 23 2n

m1 m2 m3 mn mxn

a aa ...a

A a aa ...a

... ...... ......

a aa ...a

 

 

= 

 

 

 

In compact form the above matrix is represented by A = [aij]mxn

Where aij denote ith row & jth column element.

Example 99 : Find A3x2 matrix where aij = (i + j)^2

Solution:

11 12 2 2

3 X2 21 22 2 2

31 32 2 2

a a (1 1) (1 2) 4 9

A a a (2 1) (2 2) 9 16

a a (3 1) (3 2) 16 25

   + +   

= ⇒ + + = 

     

   + +   

Example 100:Find A3 x 3 where aij =

i j; i j

i j; i j

+ < 

− ≥ 

Solution:

11 12 13

3 X3 21 22 23

31 32 33

a a a

A a a a

a a a

 

= 

 

 

1 1 1 2 1 3

2 1 2 2 2 3

3 1 3 2 3 3

 − + + 

= − − + 

 

 − − − 

0 3 4

1 0 5

2 1 0

 

= 

 

 