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
− −
(^) −
(^) − − − (^)