# NCERT Solutions for Class 12 Maths Chapter 4 – Determinants

NCERT Solutions for Class 12 Maths Chapter 4: Kopykitab provides NCERT Solutions For Class 12 Maths Chapter 4 Determinants, which are created by our professional faculty. All of the questions in the chapter have step-by-step solutions, and each solution has been explained using appropriate examples or formulas.

Through supplementary skill-building tasks targeted to their grade levels, skills, and interests, we strive to bring out the best in you. Download and go through the NCERT Solutions for Class 12 Maths Chapter 3 PDF!

## Download NCERT Solutions for Class 12 Maths Chapter 4: Determinants PDF

Calculating the determinant of a 2×2 matrix, 3×3 matrix, assessing the area of the triangle, and finding the equation of the line using determinant, minors, and co-factors are all problems covered by NCERT Solutions in Chapter 4 Maths Class 12.

### Access Determinant Class 12 NCERT Solutions PDF

Class-12-Mathematics-Solutions-Chapter-4 pdf

Practicing these Determinants Class 12 NCERT Solutions will aid you in the board exam preparation in such a way that even the most difficult questions from this chapter will appear to be simple. Scroll down to know more!

## What will you get in Class 12 Maths Chapter 4 Determinants NCERT Solutions?

The chapter comes packed with 6 exercises along with miscellaneous exercises thus including all the essential elements associated with the topic. Let us check the subtopic covered in this chapter now-

 4.1 Introduction 4.2 Determinant 4.3 Properties of determinant 4.4 Area of triangle 4.5 Minors and cofactors 4.6 Adjoint and inverse of the matrix 4.7 Application of determinants and matrices

Determinants Class 12 NCERT Solutions Exercises follows:

 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 Exercises 19 Questions (15 Long, 1 Short, 3 MCQs)

### Determinants Class 12 NCERT Solutions: 4.1: Introduction

The previous chapter already taught pupils about placing the system in a proper linear equation format in matrices. Also, they studied some other important details in the last chapter. The first intro portion will offer a brief recap which will help them to understand this chapter better.

### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants: 4.2: Determinants

The section covers the-

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

The section provides a lesson in calculating the determinant of a square matrix in a different row, for instance, the one, two, or three with easy examples.

### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants: 4.3: Properties of Determinants

As the title suggests, this segment will offer detailed notions about the properties of determinants thus simplifying the calculation by acquiring the maximum number of zeros in a row or in a column. These properties are applicable for every determinant of any order. But this chapter only states determinants of order three.

### NCERT Solutions – Class 12 Maths Chapter 4 – Determinants: 4.4 Area of Triangle

Students can calculate the area of a triangle with the help of the formulas when the coordinates of three vertices have been given. The portion covers finding the area of a triangle by metrifying the points into a determinant.

### NCERT Solutions – Class 12 Maths Chapter 4 – Determinants: 4.5 Minors and Cofactors

This portion covers the concept of expansion of determinant in compact form with minors and cofactors after finishing the problems in the chapters.

### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants: 4.6 Adjoint and Inverse of a Matrix

Once students complete the last section, they will get a clear picture of this portion and will be able to find the inverse of the matrix using adjoint. Make sure to go through the theorems and formulas to have a thorough idea of the concept.

### NCERT Solutions for Class 12 Maths Chapter 4 – Determinants: 4.7: Application of Determinants of Matrices

The section covers all the elaboration about the application of matrices thus explaining the topic of solving the linear equation in two or three variables. This area also teaches the student about the consistency of the system of the linear equation.

## NCERT Solutions for Class 12 Maths Chapter 4 – Determinants: Theorems and formulas to follow

• 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.

## Advantages of Determinants Class 12 NCERT Solutions

Why one should opt for NCERT Solutions for Class 12 Maths Chapter 4 – Determinants? You should always look out for benefits to go with anything new. Let’s find out-

1. With Solutions for Class 12-Maths, you will get an in-depth idea about the chapter which will help them finish the chapter very soon.
2. The more you run through the content the better understanding you will acquire concerning the chapter. It will not only help you for the 12th board’s exam but will also help you crack several competitive exams in the upcoming days.
3. It offers you more time and efficiency to study hard and rank better.
4. NCERT Maths Solutions would assist students in solidifying their understanding of math topics.
5. The study material is styled and curated by professionals to impart what is best suited to the students.

We have jotted down all the necessary updates concerning the upcoming 12th boards. NCERT Solutions for Class 12 Maths-Chapter 4 – Determinants is to help you with chapter 4. We wish you do great in your CBSE finals. Also, we are always here to help you out.

### How many exercises are there in Chapter 4 of the NCERT textbook for Class 12 Maths?

In total, there are six exercises in Chapter 4 of Class 12 Maths.

### How many questions are there in NCERT Maths Chapter 4 Miscellaneous Exercise?

There are a total of 19 questions (15 Long, 1 Short, 3 MCQs) in NCERT Maths Chapter 4 Miscellaneous Exercise.

### Can I get an overview of the NCERT Solutions for Class 12 Maths Chapter 4 exercises?

Yes. Go through the above blog for an overview of the NCERT Solutions for Determinants Class 12 exercises.

### Are NCERT Solutions for Class 12th Maths Chapter 4 sufficient for board examinations preparation?

Yes. NCERT Solutions for Class 12 Maths Chapter 4 covers all the topics of determinants which is sufficient for board examinations preparation.

### Where can I get Maths Chapter 4 Class 12 NCERT solutions?

You can download Maths Chapter 4 Class 12 NCERT solutions from the above blog.

### Is NCERT Solutions Class 12 Maths Chapter 4 helpful?

Yes, the NCERT Ch. 4 exercises are addressed by subject matter experts which is described in easy-to-understand language.