# NCERT Solutions Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants explains the fundamental concepts and applications of determinants. Determinants are an essential part of math studies that have multiple applications. For every square matrix, we have a function that can associate a real or complex number with it is known as a determinant. This concept is applied to determine if a system of equations has a unique solution or not. Apart from this, determinants have broad uses in engineering, science, economics, social science, etc. Thus, attaining a deep knowledge of this topic and its applications is highly crucial. NCERT Solutions Class 12 Maths Chapter 4 helps students to acquire a fundamental understanding of determinants.

The primary objective of these solutions is to provide appropriate learning of all the core concepts for students to not only score well on their boards but also to build a profound understanding of all the fundamental topics. With the regular practice of Class 12 Maths NCERT Solutions Chapter 4, students will quickly gain a deep understanding of this topic. To learn and practice with NCERT Solutions Chapter 4 Determinants, download the exercises provided in the links below.

- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.1
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.2
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.3
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.4
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.5
- NCERT Solutions Class 12 Maths Chapter 4 Ex 4.6
- NCERT Solutions Class 12 Maths Chapter 4 Miscellaneous Exercise

## NCERT Solutions for Class 12 Maths Chapter 4 PDF

A determinant of a square matrix is a scalar obtained by the product of the diagonal elements. These determinants are very useful in the analysis and solution of systems of linear equations. NCERT Solutions for Class 12 Maths Chapter 4 are meticulously formulated guides that promote the fundamental understanding of the representation of determinants along with their properties and applications. To practice with these solutions, click on the links of the pdf files given below.

**ā** Download Class 12 Maths NCERT Solutions Chapter 4 Determinants

**NCERT Class 12 Maths Chapter 4 **

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

NCERT solutions Class 12 Maths Chapter 4 Determinants are highly competent guides that efficiently impart the complete knowledge of topics related to determinants like minors and their applications. These reliable learning resources are efficient to impart a deep understanding of concepts to strengthen core skills. The language used in these solutions is quite simple for in-depth study of all topics. To practice the exercise-wise NCERT Solutions Class 12 Maths Determinants, try the links given below.

- Class 12 Maths Chapter 4 Ex 4.1 - 8 Questions
- Class 12 Maths Chapter 4 Ex 4.2 - 16 Questions
- Class 12 Maths Chapter 4 Ex 4.3 - 5 Questions
- Class 12 Maths Chapter 4 Ex 4.4 - 5 Questions
- Class 12 Maths Chapter 4 Ex 4.5 - 18 Questions
- Class 12 Maths Chapter 4 Ex 4.6 - 16 Questions
- Class 12 Maths Chapter 4 Miscellaneous Ex - 19 Questions

ā Download CBSE Class 12 Maths Chapter 4 NCERT Book

**Topics Covered:** NCERT Solutions Class 12 Maths Chapter 4 mainly focuses on the various properties of determinants, minors, cofactors, applications of determinants in finding the area of a triangle, adjoint, inverse of a square matrix, consistency, and inconsistency of system of linear equations, and solution of linear equations in two or three variables using the inverse of a matrix.

**Total Questions:** Class 12 Maths Chapter 4 Determinants has 68 questions in 6 exercises along with 19 more provided in a miscellaneous exercise. Out of these 68 questions, there are long answers, short answers and MCQs provided in each exercise to cover all important topics from an exam point of view.

## List of Formulas in NCERT Solutions Class 12 Maths Chapter 4

Determinants are considered as one of the basic maths concepts with many algebraic applications. Learning the concept of determinants is especially useful in solving a set of linear equations. It is also applied in calculating the values of square matrices. Finding the determinants of a matrix requires a basic understanding of the terms, definitions, rules, and properties of determinants. Thus, it is vital to gain a deep knowledge of all these fundamentals before solving the problems provided in each exercise of this chapter. NCERT Solutions Class 12 Maths Chapter 4 elaborates each of these terms with the help of interactive illustrations. Some of the important terms and definitions explained in these NCERT Solutions for Class 12 Maths Chapter 4 are given below.

**Determinant:**To any square matrix P = [p_{ij}] of order n, there is a number associated called the determinant of the square matrix P, where p_{ij}= (i, j)th element of P.

**Determinant of a matrix of order one:**If P = [ p ] is a matrix of order 1, then the determinant of P is equal to p.

**Minor:**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}Minor of an element a_{ij}is denoted by M_{ij}.

**Adjoint of a matrix:**The adjoint of a square matrix A = [a_{ij}]n × n is defined as the transpose of the matrix [A_{ij}]n × n, where A_{ij}is the cofactor of the element a_{ij}. The adjoint of matrix A is denoted by adj A.

## FAQs on NCERT Solutions Class 12 Maths Chapter 4

### What is the Importance of NCERT Solutions for Class 12 Maths Chapter 4 Determinants?

NCERT Solutions for Class 12 Maths Chapter 4 Determinants are comprehensive guides efficient to deliver deep conceptual knowledge of all basics. By planning a strategic exam preparation with the help of these resources students can attain a thorough understanding of all topics. The well-framed structure of solutions is prominent to raise the mathematical learning and confidence in students. Practicing with these resources also promotes a sense of self-accomplishment required to face various competitive exams.

### What are the Important Topics Covered in NCERT Solutions Class 12 Maths Chapter 4?

Chapter 4 Determinants of class 12 Maths briefly defines all the important applications and uses of Determinants in various subjects and disciplines. All topics covered in the NCERT Solutions Class 12 Maths Chapter 4 are equally important as they provide information on different aspects of determinants. Questions in these solutions are quite beneficial to enhance the fundamental understanding of determinants. The objective of curating these solutions is to promote the math potential of kids to help them accomplish their goals.

### Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Determinants?

Practicing all the questions included in NCERT Solutions Class 12 Maths Determinants gives a step-by-step knowledge of each topic. Problems in these solutions are well-placed at a gradually increasing level to help students comfortably adjust to the rising complexity. Kids can quickly grasp the core fundamentals of determinants as well as their applications by solving and practicing these sums. Learning with these solutions is also beneficial in preparing for various competitive exams and higher-level studies.

### How Many Questions are there in Class 12 Maths NCERT Solutions Chapter 4 Determinants?

Class 12 Maths Chapter 4 Determinants has 87 questions in 7 exercises. Practicing these questions ensures an accurate and clear understanding of this topic. Students can also plan systematic learning of these exercises, and concepts based on determinants. The lucid format of these solutions is efficient in acquiring a sound knowledge of the operations that can be determinants.

### What are the Important Formulas in NCERT Solutions Class 12 Maths Chapter 4?

NCERT Solutions Class 12 Maths Chapter 4 mainly focuses on the Determinants, their properties, and applications. Some of the important concepts explained in these solutions are based on the properties of determinants. These topics are covered in detail with the help of examples and illustrations. The solutions are more focused on imparting a precise conceptual understanding of the fundamentals as well as building the skills required to solve complicated sums.

### Why Should I Practice NCERT Solutions for Class 12 Maths Chapter 4 Determinants?

NCERT Solutions for Class 12 Maths Chapter 4 Determinants is a competent learning resource that offers complete guidance and practice of core concepts for higher-level studies. These solutions cover the whole syllabus of CBSE Class 12 Maths Chapter 4 to provide comprehensive learning of all topics. The format of these solutions is pretty convenient to clear doubts and learn complex concepts. With the thorough practice of these resources, students can ensure good results in their annual maths exam.