APPLICATIONS OF MATRICES AND DETERMINANTS

APPLICATIONS OF MATRICES AND DETERMINANTS

Applications of Matrices and Determinants”

Below the title, the chapter is divided into five sections, each covering a specific concept:

1.1 Introduction

This section gives the basic idea of matrices, determinants, and why they are useful in mathematics.

1.2 Inverse of a Non-Singular Square Matrix

This part explains how to find the inverse of a square matrix (a matrix with equal number of rows and columns), provided it is non-singular (determinant ≠ 0).

1.3 Elementary Transformations of a Matrix

This explains row and column operations (like swapping rows, multiplying a row by a constant, adding a row to another). These transformations are used to simplify matrices.

1.4 Applications of Matrices: Solving System of Linear Equations

This section teaches how to use matrices to solve linear equations such as:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Using matrix methods like inverse matrix method.

1.5 Applications of Matrices: Consistency of System of Linear Equations by Rank Method

This explains how to find whether a system of equations has:

• a unique solution,

• no solution, or

• infinitely many solutions,
  using the rank of a matrix.