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