NCERT SOLUTIONS FOR CLASS 12 MATHS CHAPTER 4

4.1 Introduction

Students have already read about how to represent a system of linear equations using matrices and the condition to know whether this system has a unique solution or not based on the determinant. These things will be revised under this section.

4.2 Determinant

4.2.1 Determinant of a matrix of order one

4.2.2 Determinant of a matrix of order two

4.2.3 Determinant of a matrix of order 3 × 3

In this section, students will learn how to find the determinant of a square matrix of different orders such as one, two and three along with examples.

4.3 Properties of Determinants

In the previous section, students have learnt how to expand the determinants. In this section, they will study some properties of determinants which simplifies its evaluation by obtaining the maximum number of zeros in a row or a column. These properties are correct for determinants of any order. However, in this chapter, it has been limited up to determinants of order three only.

4.4 Area of a Triangle

We can find the area of a triangle using the formula when the coordinates of three vertices have been given. In this section, you will learn how to find the area of the triangle by converting the points in the form of a determinant.

4.5 Minors and Cofactors

Students will learn to write the expansion of a determinant in compact form using minors and cofactors after practicing the problems in this section.

4.6 Adjoint and Inverse of a Matrix

4.6.1 Adjoint of a matrix

After solving the problems in this section, you will understand clearly how to find the inverse of a matrix using adjoint. Many theorems and examples are given under this section to enhance your skills.

4.7 Applications of Determinants and Matrices

4.7.1 Solution of system of linear equations using inverse of a matrix

Here, you will get a complete description of applications of determinants and matrices for solving the system of linear equations in two or three variables and how to check the consistency of the system of linear equations.