  # NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions For Class 12 Maths Chapter 4 Determinants are available at CoolGyan’S which are given by our expert faculty. The step by step solutions for all the questions enlisted under the chapter and each solution has been explained using suitable examples or formulas. Maths Class 12 NCERT Solutions are written by considering the marking scheme. CoolGyan’S aims to bring out the very best in students through additional skill-building exercises that are tailored to their grade levels, abilities and interests.

A determinant is a number that can be calculated for only square matrices. In solving a system of linear equations, determinant plays an important role to check whether the system of equations has a unique solution or not. It has many applications in science, engineering, social sciences, and economics, etc., NCERT Solutions of this chapter of Class 12 cover all the problems such as finding the determinant of a 2×2 matrix,  3×3 matrix, evaluating the area of the triangle, finding the equation of the line using determinant, minors, and co-factors. Also, calculating the determinant using minor and co-factor, adjoint, and the inverse of a matrix. Besides, finding the solution of equations and determinant as the sum of two or more determinants.

### Access Answers of Maths NCERT Chapter 4 Determinants                                                                                   Also Access NCERT Exemplar for Class 12 Maths Chapter 4 CBSE Notes for Class 12 Maths Chapter 4

### NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Chapter Determinants has a total of 6 exercises and a miscellaneous exercise which covers all the questions related to the chapter. The topics discussed in Chapter 4 NCERT Solutions For Class 12 of Maths includes:

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

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.

Exercise 4.1 Solutions: 8 Questions (2 Long, 5 Short Answers, 1 MCQ)

Exercise 4.2 Solutions: 16 Questions(7 Long, 7 Short, 2 MCQs)

Exercise 4.3 Solutions: 5 Questions ( 4 Short Answers, 1 MCQ)

Exercise 4.4 Solutions: 5 Questions (4 Long, 1 MCQ)

Exercise 4.5 Solutions: 18 Questions (11 Long, 5 Short, 2 MCQs)

Exercise 4.6 Solutions: 16 Questions (13 Long, 3 Short)

Miscellaneous Exercise Solutions: 19 Questions (15 Long, 1 Short, 3 MCQs)

### Key Features of NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Class 12 NCERT Solutions of CoolGyan’S for Chapter 4 cover the following points and formulas.

• If any two rows or any two columns are identical or proportional, then the value of the determinant is zero
• A square matrix A has an inverse if and only if A is non-singular
• Unique solution of equation AX = B is given by X = A–1 B, where A ≠ 0
• If a system of equation is consistent, then it has a solution
• If a system of equations is inconsistent, then there is no solution
• For a square matrix A in matrix equation AX = B:

If | A| ≠ 0, then there exists a unique solution

If | A| = 0 and (adj A) B ≠ 0, then there exists no solution

If | A| = 0 and (adj A) B = 0, then system may or may not be consistent

## Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 4

### How many problems are there in NCERT Solutions for Class 12 Maths Chapter 4?

Exercise 4.1 of NCERT Solutions has 8 questions, Exercise 4.2 has 16 questions, Exercise 4.3 and 4.4 has 5 questions, Exercise 4.5 has 18 questions, Exercise 4.6 has 16 questions and miscellaneous exercise has 19 questions. Long answers, short answers and MCQs are present in each exercise covering the topics which are important from the exam point of view. The solutions for the exercise wise problems are designed by a set of experts at CoolGyan’S having vast conceptual knowledge.

### What are the uses of determinants according to NCERT Solutions for Class 12 Maths Chapter 4?

Determinants is one of the main concepts having a number of applications in algebra. This concept is useful to solve a set of linear equations. Using determinants, students will be able to understand the change in area, volume, variables in terms of integrals. It can also be used to calculate the values of square matrices.

### What kind of problems can I expect in the board exams from NCERT Solutions for Class 12 Maths Chapter 4?

The problems based on solving the given set of linear equations using determinants can be expected from this chapter. Proofs that can be derived using the theory of determinants and prove that sums are also important from the exam perspective. In certain problems, you should determine the values of unknown variables using determinants and their resultant values.