TABLE OF CONTENTS Determinants owe their birth to the technique of solving simultaneous linear equations. A large number of physical phenomena are governed by linear differential equations which are solved by reducing them into a system of simultaneous linear equations.
Matrices originated as mere stores of information but, at present, have found very wide application. They play a very vital role not only in mathematics but also in communication theory, network analysis, theory of structures, quantum mechanics, biology, sociology, economics, psychology, and statistics.
Determinants and matrices play the key role in providing suitable criteria for testing the consistency or otherwise of a system of linear equations.
In this chapter, we will deal first with determinants and then with matrices.
DETERMINANTS
Let us eliminate x and y from the equations
The eliminant is
or
which is conveniently written in the compact form 
In other words, we have 
The expression 
is called a determinant of the second order. The numbers a 1, b 1, a 2, b 2 are called the elements of the determinant. a 1 b 2 a 2 b 1 is called the expansion or the value of the determinant.
We notice that a determinant of the second order is a block of 2 2 elements arranged in the form of a solid square along two horizontal lines (called rows) and two vertical lines (called columns) and is bounded by two...
