NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3 Determinants - PDF Download

NCERT solutions for class 12 maths chapter 4 exercise 4.3 Determinants explain an essential topic of minors and cofactors of determinants. This exercise will cover the definitions of minors and cofactors and the terms related to them. Minors and cofactors are important concepts to understand the complex questions asked in ex 4.3. Class 12 maths chapter 4 exercise 4.3 NCERT solutions are developed by the academic team of mathematics at eSaral to provide a deep knowledge of this topic. 

Ex 4.3 class 12 maths chapter 4 has a total of 5 questions as well as some examples based on the minors and cofactors of determinants. By solving these questions, you will be able to get a precise understanding of the topic. Ex 4.3 class 12 maths solutions are also available in PDF format. You can download the free PDF of NCERT solutions from the official website of eSaral and practice the questions to score good marks in exams.     

Topics Covered in Exercise 4.3 Class 12 Mathematics Questions

Ex 4.3 class 12 maths ch 4 covers the important topic of minors and cofactors of determinants. You will get the detailed explanation of this topic provided by subject experts of eSaral.

1. Minors and Cofactors

Minors -  Minor of an element a_ij of a determinant is the determinant obtained by deleting its ith row and jth column in which element a_ij lies. Minor of an element aij is denoted by M_ij. 

Minor of an element of a determinant of order n(n ≥ 2) is a determinant of order n – 1.

Cofactors - Cofactor of an element a_ij , denoted by A_ij is defined by

                        A_ij = (–1)^{i + j} M_ij , where Mij is minor of a_ij.

If elements of a row (or column) are multiplied with cofactors of any other row (or column), then their sum is zero.

Tips for Solving Exercise 4.3 Class 12 Chapter 4 Determinants

NCERT solutions for ex 4.3 class 12 maths chapter 4 Determinants has questions related to minors and cofactors of determinants. These questions can be solved by following the tips and tricks provided by expert teachers of eSaral. Here are some of them mentioned below.

1. First of all you must learn the terms, definitions and concepts associated with minors and cofactors of determinants to form a clear understanding of concepts.

2. You should practice and revise the questions in repetition to be well versed with the nature of questions.

3. Examples based on the topic are also provided in NCERT solutions class 12 maths chapter 4 ex 4.3 which you must go through to have a precise understanding of exercise questions.
   

Importance of Solving Ex 4.3 Class 12 Maths Chapter 4 Determinants

Our subject experts have combined some benefits of solving ex 4.3 questions for class 12 maths chapter 4 which are mentioned below.

1. NCERT solutions class 12 maths chapter 4 ex 4.3 helps you when you are unable to solve questions on your own.

2. Ex 4.3 class 12 maths ch 4 NCERT solutions are explained precisely with simple language that helps you to comprehend the concepts while solving the questions.

3. All the questions of ex 4.3 class 12 maths ch 4 are solved with step by step methods in NCERT solutions that will help you to comprehend the questions and score high marks in board exams.

4. Answers for ex 4.3 questions are provided in accurate format and precise manner which can be trusted without any doubt to prepare for exams.

Frequently Asked Questions 

Question 1. What do you understand by minors of determinants in ex 4.3 class 12 maths chapter 4?

Answer 1. Minor of an element aij of a determinant is the determinant obtained by deleting its ith row and jth column in which element a_ij lies. Minor of an element a_ij is denoted by M_ij . 

Question 2. What is the formula to find the cofactor of determinants?

Answer 2. The formula to find the cofactor of an element aij is given by A_ij = (–1)^{i + j} M_ij  , where M_ij is minor of a_ij .