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Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 4 Determinants, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and help in entrance examinations like JEE mains and NEET.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

There are six exercises in Chapter Determinants, plus a miscellaneous exercise that includes all of the chapter’s questions. The following topics are covered in Chapter 4 NCERT Exemplar Solutions for Class 12 Maths Term I:

**4.1 Introduction**

Students have already learned how to use matrices to represent a system of linear equations and how to use the determinant to determine whether or not this system has a unique solution. This section will be changed to include these items.

**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

Students will learn how to find the determinant of a square matrix of various orders, such as one, two, and three, as well as examples, in this section.

**4.3 Properties of Determinants**

Students learnt how to expand the determinants in the previous part. In this section, they will look at certain determinant qualities that make evaluating them easier by determining the greatest number of zeros in a row or column. These principles hold true for any order of determinants. However, it has only been applied to determinants of order three in this chapter.

**4.4 Area of a Triangle**

When the coordinates of three vertices are supplied, we may use the formula to get the area of a triangle. You’ll learn how to find the area of a triangle by translating the points into a determinant in this section.

**4.5 Minors and Cofactors**

After working through the problems in this part, students will be able to write the expansion of a determinant in compact form using minors and cofactors.

**4.6 Adjoint and Inverse of a Matrix**

**4.6.1** **Adjoint of a matrix**

After working through the exercises in this section, you’ll have a firm grasp on how to use an adjoint to obtain the inverse of a matrix. This section contains several theorems and examples to help you improve your skills.

**4.7 Applications of Determinants and Matrices**

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

In these NCERT Exemplar Solutions, you will get a detailed explanation of how to use determinants and matrices to solve systems of linear equations in two or three variables, as well as how to assess the system’s coherence.

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 Exemplar Solutions for Class 12 Maths Chapter 4 Determinants**

The **NCERT Exemplar Solutions Class 12** of Infinity learn for Chapter 4 covers the following points and formulas.

- The value of the determinant is zero if any two rows or columns are identical or proportionate.
- A matrix that is square. If and only if A is non-singular, it has an inverse.
- Unique solution of equation AX = B is given by X = A–1 B, where A ≠ 0
- A system of equations has a solution if it is consistent.
- There is no solution if a system of equations is inconsistent.
- 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 Question**

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

Ans: Exercise 4.1 has 8 questions, Exercise 4.2 has 16 questions, Exercises 4.3 and 4.4 have 5 questions, Exercise 4.5 has 18 questions, Exercise 4.6 has 16 questions, and the miscellaneous exercise has 19 questions. Long answers, short answers, and MCQs are included in each assignment, and they cover the areas that are important for the first term test. A team of infinity learn professionals with broad conceptual understanding creates the solutions for the exercise-specific issues.

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

Determinants are a key subject in algebra that has a variety of applications. This notion can be applied to the solution of a collection of linear equations. Students will be able to understand the change in the area, volume, and variables in terms of integrals using determinants. It can also be used to calculate square matrices' values.

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

This chapter will cover issues using the use of determinants to solve a set of linear equations. Proofs that can be derived using determinant theory and show that sums are also essential from the perspective of the term – I exam. You should use determinants and their resulting values to determine the values of unknown variables in some instances.

##### Why Opt for Infinity Learn?

In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.

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