Paper 4: Fundamentals of Business Mathematics & Statistic

2.66 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS

Algebra

Singular and Non Singular Matrix

If detA = 0 for square matrix, then it’s a singular matrix.

If detA ≠ 0 for square matrix, then it’s a non singular matrix.

Sub Matrix

If a finite number of rows or columns are deleted in a matrix then the resulting matrix is known as a sub

matrix

Example 111 : A =

3 2 4

5 6 7

8 2 1

 

 

 

 

After the deletion of first row and first column of matrix A following sub matrix B obtain, where

B =

6 7

2 1

 

  

Example 112: If A =

3 5

7 6

, find |A|

|A| = 3 x 6 – 7 x 5

= 18 – 35 ⇒ −17

Example 113 : If A =

1 2 3

4 5 6

7 8 9

 

 

 

 

, find |A|

Solution: |A|

1 5 6 2 4 6 3 4 5

8 9 7 9 7 8

=      − +

          

= 1(45 – 48) –2(36 – 42) + 3(32 – 35)

= 1(–3) –2(–6) + 3 (–3)

= – 3 + 12 – 9

= 0

Example 114 : Find the determinant of the given 3×3 matrix

2 3 2

6 3 3

2 3 2

− −

(^) −
(^) − − − (^)