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Subject specialists have created NCERT Solutions for Class 12 Maths Chapter 4 Determinants, including thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Solutions for Class 12 provide useful solutions for improving conceptual knowledge.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in exams but also in 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 is essential for getting the best results when answering questions.

## Maths Class 12 NCERT Solutions Chapter 4 Exercises |

Exercise 4.1 Class 12 Maths |

Exercise 4.2 Class 12 Maths |

Exercise 4.3 Class 12 Maths |

Exercise 4.4 Class 12 Maths |

Exercise 4.5 Class 12 Maths |

Exercise 4.6 Class 12 Maths |

Miscellaneous Exercise on Chapter 4 Class 12 |

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

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 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 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 learned how to expand the determinants in the previous part. This section 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 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 of using 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 a system of linear equations using the inverse of a matrix**

In these NCERT 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 and 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 Solutions for Class 12 Maths Chapter 4 Determinants

The **NCERT 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 square matrix. 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 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 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 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 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 Solutions for Class 12 Maths Chapter 4?

This chapter will cover issues using determinants to solve a set of linear equations. Proofs derived using determinant theory show that sums are also essential from the perspective of the term – I exam. It would help if you used determinants and their resulting values to determine the values of unknown variables in some instances.