Page 124 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

Notes
2x 5y 85 and 3x 8y 132
2 5
16 15 1
3 8

85 5
680 660 20
1
132 7

2 85
264 255 9
2
3 132
20
x 1 20
1

9
y 2 9
1
The price of Rice is 20 per kg and the price of Wheat is 9 per kg.

4.11 Summary

To every square matrix A, a real number is associated. This real number is called its
determinant.

It is denoted by ( ).A
The minor of an element of a square matrix A is defined to be the determinant obtained by
deleting the row and column in which the element is present.

The cofactor of an element of a square matrix is defined to be ( 1) i j (minor of the
element) where i and j are the number of row and column in which the element is present.
The adjoint of a square matrix A is the transpose of the matrix of the cofactors of the
elements of A and is denoted by Adj. A.
A square matrix A is said to be singular if | | 0A and is said to be non-singular if | | 0.A
Inverse of a square matrix is defined if and only if it is non-singular. The inverse of a non-
singular square matrix A is denoted by A 1 .
In this unit we have studied the concepts of determinants and their importance in solving
real world problems of business.
A determinant is a scalar associated with a square matrix.

4.12 Keywords

Cofactor: A cofactor of an element a , denoted by C , is its minor with appropriate sign.
ij ij
Determinant: A numeric value that indicate singularity or non-singularity of a square matrix.

Minor: A minor of an element a denoted by M , is a sub-determinant of A obtained by
ij ij
deleting its i row and j column.
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