Paper 4: Fundamentals of Business Mathematics & Statistic

2.60 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Multiplication of two matrices

The Product AB of two matrices A and B is defined only if the number of columns in A is equal to the number

of rows in B. If A is of order m x n and B is of order n x s. Then order of AB is m x s

To multiply A with B, elements of the ith row of A are to be multiplied by corresponding elements of jth

column of B and then their sum is taken

i.e. If A

11 12 13 11 12 13

21 22 23 21 22 23

31 32 33 31 32 33

a a a b b b

a a a & B b b b

a a a b b b

   

=  =  

   

   

Then AB

11 11 12 21 13 31 11 12 12 22 13 32 11 13 12 23 13 33

21 11 22 21 23 31 2112 22 22 23 32 2113 22 23 23 33

31 11 32 21 33 31 31 12 32 22 33 32 31 13 32 23 33 33

a b a b a b a b a b a b a b a b a b

a b a b a b a b a b a b a b a b a b

a b a b a b a b a b a b a b a b a b

+ + + + + +

=^ + + + + + +^

(^) + + + + + + (^)
Example 103 : Evaluate AB where A = [1 3 2]1x3 B
3 x1

4

1

7

 

= 

 

  

Solution: AB = [1 X 4 + 3 X 1 + 2 X 7]1x1

= [21]

Example 104 : Evaluate AB where A

3 x 2

2 3

4 5

6 7

 

= 

 

  

B

2 x 3

1 3 5

2 4 6

= 

 

Solution:AB =

2x1 3x2 2x3 3x4 2x5 3x6

4x1 5x 2 4x3 5x4 4x5 5x6

6x1 7x2 6x3 7x4 6x5 7x6

 + + + 

 + + + 

 

 + + + 

=

8 18 28

14 32 50

20 46 72

 

 

 

 

Example 105 : Evaluate AI where A =

3 2

4 7

 

  

Solution:AI =

3 2 1 0 3x1 2x0 3x 0 2x1

4 7 0 1 4x1 7x0 4x 0 7x1

    ⇒ + + 

         + + 

=

3 2

4 7

 

  