Page 79 - DMTH201_Basic Mathematics-1

Basic Mathematics – I Pankaj Kumar, Lovely Professional University

Notes Unit 4: Determinants

CONTENTS
Objectives
Introduction

4.1 Determinant of a Square Matrix
4.2 Minor of an Element of a Square Matrix
4.3 Cofactor of an Element of a Square Matrix

4.4 Adjoint of a Square Matrix
4.5 Singular and Non-singular Matrices
4.6 Inverse of a Square Matrix
4.7 Solution of a System of Linear Simultaneous Equations (Cramer’s Rule)
4.8 Examples on Adjoint and Inverse

4.9 Examples on Simultaneous Equations (Cramer’s Rule)
4.10 Examples of Business Application of Matrices
4.11 Summary

4.12 Keywords
4.13 Self Assessment
4.14 Review Questions
4.15 Further Readings

Objectives

After studying this unit, you will be able to:

Explain the meaning of determinants
Discuss matrix representation of a linear equation system
Describe inverse of a matrix using determinants

Understand solution of equations
Introduction

A determinant was first introduced to solve systems of linear equations. In 1750, G. Cramer gave
a rule called Cramer's rule to solve the simultaneous equations. In the previous unit, we have
studied about matrices and algebra of matrices. We have also learnt that a system of algebraic
equations can be expressed in the form of matrices.

In this unit, we shall study determinants up to order three only with real entries. Also, we will
study minors, cofactors and applications of determinants in finding the area of a triangle, adjoint
and inverse of a square matrix, consistency and inconsistency of system of linear equations and
solution of linear equations in two or three variables using inverse of a matrix.

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