**Table of content**

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

Maths is especially important for engineering aspirants, NCERT solutions for class 12 maths chapter 4 provided which help you to solve the unsolved problems of the class 12 NCERT maths book prescribed by the CBSE helpful in board exams and competitive entrance exams. The NCERT solutions break down into detailed steps and explain the answer, which helps you to understand the pattern of questioning. These solutions not only help in having your basics clear but also help in improving your problem-solving abilities.

The NCERT solutions for class 12 maths chapter 4 are prepared by experts. It covers all the concept of the subject to help you in scoring higher marks. During solving the problems if you have doubts, we have a team of teachers who solve your doubts any time.

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

In NCERT solutions for class 12 maths chapter 4, you will learn to evaluate determinant of a 2×2 matrix, 3×3 matrix, area of triangle, equation of line using determinant, minors, and cofactors, evaluating determinant using minor and co-factor, adjoint and inverse of a matrix, find solution of equations, determinant as sum of two or more determinants.

**Sub-topics covered under NCERT Solutions for Class 12 Maths Chapter 4**

- 4.1 – Introduction
- 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

- 4.3 – Properties of Determinants
- 4.4 – Area of a Triangle
- 4.5 – Minors and Cofactors
- 4.6 – Adjoint and Inverse of a Matrix
- 4.6.1 -Adjoint of a matrix

- 4.7 – Applications of Determinants and Matrices
- 4.7.1 – Solution of a system of linear equations using the inverse of a matrix

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

In NCERT solutions for class 12 maths, chapter 4 calculate determinants, solve matrix using different properties of determinants, area of a triangle, adjoint and the inverse of a matrix, applications of determinants and matrix. Let us now discuss the subtopics include in NCERT solutions for class 12 maths chapter 4.

**4.1 – Introduction **

In this, you will get a brief introduction to determinants and relation between determinants and matrices.

**4.2 – Determinant **

In this, you will study the determinants and its types.

**4.2.1 – Determinant of a matrix of order one **

In this, you learn to solve the matrix of order one.

**4.2.2 – Determinant of a matrix of order two **

In this, you learn to solve the matrix of order two.

**4.2.3- Determinant of a matrix of order 3 × 3 **

In this, you learn to solve the matrix of order 3 × 3.

**4.3 – Properties of Determinants**

** **In this, you will understand the different properties of determinants and some important results of determinants.

**4.4 – Area of a Triangle **

In this, you will evaluate the area of a triangle in terms of determinants.

**4.5 – Minors and Cofactors **

In this, you will learn about the minor of determinants and their formation, concept of cofactors, properties of minors and cofactors.

**4.6 – Adjoint and Inverse of a Matrix **

In this, you learn about the adjoint which is a transpose of the matrix of cofactors, inverse of a matrix.

**4.6.1 -Adjoint of a matrix **

In this, you will learn to evaluate the adjoint of a matrix and theorems related to it.

**4.7 – Applications of Determinants and Matrices**

In this, you learn the various application of determinants and matrices.

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

In this, you learn to determine whether a system of equation is consistent or inconsistent according to as its solution exists or not, find a unique solution, finding a solution of the linear equation in two variables by the inverse of the coefficient matrix by Cramer’s rule, Cayley – Hamilton theorem, properties of characteristic.

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