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NCERT Solutions for Class 12 Maths Chapter 4 Determinants - PDF Download

JEE Mains & Advanced

Mathematics is a subject that often establishes mixed reactions from students. Among the various topics covered in Class 12 Mathematics, one chapter that holds both theoretical significance and practical application is Chapter 4 - Determinants. This chapter deals with matrices and their properties, a fundamental concept in higher-level mathematics.The detailed solutions to every question listed in the chapter, which is part of the CBSE syllabus. Each solution has been described using appropriate concepts or examples.To ease the learning process and aid students in mastering the topic eSaral provides well-structured solutions for Class 12 Maths Chapter 4 Determinants. 

Determinants are values associated with square matrices, providing essential information about the matrix's properties and behavior. In Chapter 4, students encounter the concept of 2x2 and 3x3 matrices, evaluating the area of the triangle, and finding the equation of the line using determinants, minors, and co-factors. They also cover problems concerning calculating the determinant using a matrix's inverse, adjoint, and minor and cofactor. Students can now use the link provided by eSaral to access the PDF of the NCERT Solutions for Class 12 Maths Chapter 4.

NCERT Solutions for Class 12 Maths Chapter 4 - Determinants I Free PDF

When students cannot understand the questions, they tend to get anxious. Students need not worry, though, as they have access to the solutions for Chapter 4 Determinants. Here, you can access appropriate solutions for chapter 4 Determinants, which have been prepared by qualified experts. The subject matter experts who developed and compiled these solutions have made them available on the eSaral website. You can obtain relevant chapter 4 Determinants Class 12 solutions right here that have been selected by expertise.

Important Topics Covered in Chapter 4 - Determinants

4.1 Introduction - The method for utilizing matrices to describe a system of linear equations and the criteria for determining whether or not this system has a unique solution based on the determinant have already been learned in the previous chapter. Here, all things will be revised in this chapter.

4.2 Determinant 

  1. Determinant of a matrix of order one

  2. Determinant of a matrix of order two

  3. Determinant of a matrix of order 3×3

This section will explain how to solve the determinant of a square matrix of different orders like one, two and  three including examples.

4.3 Area of a Triangle - When three vertices coordinates are given, you may use the formula to get an area of the triangle. Here, You can find out how to transform the points into a determinant form in order to calculate the triangle's area.

4.4 Minors and Cofactors - After working through the questions presented in this part, you will learn how to use minors and cofactors to write the expansion of a determinant in compact form.

4.5 Adjoint and Inverse of a Matrix 

  1. Adjoint of a Matrix

You will have a comprehensive understanding of how adjoint works to determine a matrix's inverse. This section contains a lot of theorems and examples to help you develop your abilities.

4.6 Applications of Determinants and Matrices

  1. Solution of System of Linear equations using Inverse of Matrix

In this section,You get a thorough explanation of how to solve a system of two or three linear equations using determinants and matrices, as well as how to determine whether the system of equations is consistent.

NCERT Solutions for Class 12 Maths Chapter 4 Exercises

For class 12 students studying Mathematics, Chapter 4 in the NCERT textbook is a crucial section. To master this chapter, the exercises provided here are a potent tool to deepen one's understanding and enhance problem-solving skills. Here, our subject experts aim to elucidate the essence of NCERT Class 12 Chapter 4 exercises, empowering students to conquer this mathematical frontier with confidence and ease.

The exercises from chapter 4 Determinants are listed in the section below.

Exercise 4.1

8 Questions & Solutions

Exercise 4.2

5 Questions & Solutions

Exercise 4.3

5 Questions & Solutions

Exercise 4.4

18 Questions & Solutions

Exercise 4.5

16 Questions & Solutions

Miscellaneous Exercise

6 Questions & Solutions

 Benefits of Downloading the Class 12 Maths NCERT Solutions Chapter 4 - Determinants

The chapter 4 of determinants holds significant importance in the academic journey of students. As students delve into complex concepts and problem-solving techniques, having access to reliable resources becomes essential. One such valuable resource is the NCERT Solutions for Class 12 Maths, Chapter 4 - Determinants. Here, we will explore the numerous benefits of downloading and utilizing these solutions to enhance learning and academic performance.

  1. Clarity and Complete Understanding: Our subject matter experts with in-depth understanding of the subject carefully select NCERT Solutions. Students get access to detailed explanations for each problem by downloading the Class 12 Maths NCERT Solutions for Chapter 4. 

  2. Enhance Problem-Solving Techniques: Chapter 4 of Class 12 Math covers a variety of determinants, including square matrices, their properties, and applications. Numerous practice problems with thorough solutions are offered by NCERT Solutions at eSaral. Students may develop their analytical and problem-solving skills by resolving these problems.

  3. Bridging the Gap: Bridging the gap between theoretical concepts taught in the classroom and practical implementations in real-world situations is the goal of NCERT Solutions. Learning becomes more interesting when instructors give students relevant examples and applications so they may make connections and understand determinants.

  4. Time Management: A time-saving tool is the NCERT Solutions for Class 12 Maths Chapter 4 provided on eSaral. Students are able to efficiently manage their time during examinations because of the shortcuts and solutions they offer for solving determinants.

  5. Accurate and Verified Solutions: In mathematics, accuracy is essential since even small mistakes can have vastly different outcomes. Our subject specialists rigorously check the accuracy of the NCERT Solutions pdf. Students can create a solid foundation in mathematics by obtaining these solutions so they can be ensured they are learning from authentic and dependable sources.

Frequently Asked Questions

Question 1. Why do we use determinants according to NCERT solutions chapter 4?

Answer 1. Determinants are one of the key concepts in algebra with many applications. For the purpose of solving a set of linear equations, this concept is essential. Students will be able to comprehend the change in area, volume, and variables in terms of integrals using determinants. It can also be used to figure out square matrices' value.

Question 2. How many exercises are there in chapter 4 Determinants?

Answer 2. There are five exercises in total in chapter 4 Determinants. The last exercise of chapter 4 is miscellaneous exercise.


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