NCERT Solutions Class 12 Mathematics Chapter 4 Determinants is available online for the students to refer to and study on Extramarks. The chapter introduces determinants, their properties, and their applications. In addition, the chapter also includes various problems and a step-by-step solution to each problem that aids students in understanding the concept better. Furthermore, the solutions are built on the CBSE syllabus of the latest academic year and with reference to NCERT.
A determinant is a number that can only be calculated with the help of square matrices. If the students want to score more in linear equations, then the determinant is essential to learn. It helps to check whether the system of equations has a unique solution or not. Besides, students will get a glimpse of the previous chapter, matrices. This chapter also carries essential elements and helps to improve their calculations.
In the NCERT Solutions Class 12 Mathematics Chapter 4, students can understand the complex theories and formulas in an easy to understand language. These sub-topics include basic principles of determinant, cofactors, adjoint, and the inverse of a matrix. Besides, this solution has proper explanations and clear concepts to help students understand better.
Students looking for step-by-step solutions to the problems mentioned in ch 4 mathematics class 12 may register in Extramarks. Extramarks not only offers other NCERT Solutions for Class 12 but also from Class 1 to class 11. In addition, students may log in to the website for updated study material, revision notes, CBSE sample papers, important questions, and the latest notifications and news regarding CBSE exams.
Key Topics Covered In NCERT Solutions Class 12 Mathematics Chapter 4
Extramarks NCERT Solutions for Class 12 Mathematics Chapter 4 covers all essential topics under determinants. Students will start by learning how to find the determinant of a matrix of order one and the properties of determinants. More precise calculations and solutions make them understand multiplications in positives instead of negatives. There are four exercises and three subtopics under NCERT Solutions for Class 12 Mathematics Chapter 4. In addition, students can refer to the study material offered by Extramarks as it offers better solutions.
Topics covered in Chapter 4 Determinant include
| Exercise |
Topics |
| 4.1 |
Introduction |
| 4.2 |
Determinant |
| 4.3 |
Properties of Determinants |
| 4.4 |
Area of Triangle |
| 4.5 |
Minors and Cofactors |
| 4.6 |
The Adjoint and Inverse of a Matrix |
| 4.7 |
Applications of Determinants and Matrices |
4.1 Introduction
NCERT Solutions Class 12 Mathematics Chapter 4 introduces the students to Determinants and their basic concepts and theorems, wherein they will be introduced to the properties of determinants such as minors, cofactors, and applications of determinants. Further, the students will get a hold of topics like the inconsistency of the system of linear equations and solutions of linear equations.
4.2 Determinant
This is one of the crucial sections. Students will understand the grassroots concepts; as learnt in the previous Chapter 3 Matrices, any matrix inside a mode is read as a determinant of a matrix. In addition, students can learn how to find the determinant of a matrix of order one, making it easy to comprehend. Students may refer to Extramarks NCERT Solutions Class 12 Mathematics Chapter 4 as it provides straightforward and easy-to-understand calculations.
4.3 Properties of Determinants
Under this topic, students will observe that prominent examples revolve around the properties of determinants. This section elaborates on how the statement properties are true for determinants of any order. The students will get to explore six different properties of determinants. Students may refer to the exercise problems to understand the properties better. Extramarks NCERT Solutions Class 12 Mathematics Chapter 4 offers step-by-step solutions for many exercises under this topic.
4.4 Area of Triangle
This section guides students on calculating the area of triangles and the application of vertices. It also elaborates on particular topics such as positive quantity and absolute values of determinants. It also helps the students understand the positive and negative values of the determinant.
4.5 Minors and Cofactors
In the NCERT Solutions Class 12 Mathematics Chapter 4, minors, cofactors and their main concepts are covered. In addition, this section will teach the students about five more expansion ways that help calculate the area of a triangle.
4.6 The Adjoint and Inverse of a Matrix
Further in Chapter 4 Class 12, students will learn about the inverse and existence. It contains detailed explanations in terms of finding the adjoint of the matrix. There is a total of five theorems that helps to verify the concepts.
4.7 Applications of Determinants and Matrices
NCERT Solutions Class 12 Mathematics Chapter 4 covers the essential concepts in applications of determinants and matrices. A student will learn how to check the consistency of the system of linear equations. Under this topic, students will learn and study the solution system of linear equations.
For detailed study material, students may refer to Extramarks, where step-by-step solutions on essential concepts, including consistent and inconsistent systems, are provided. With the help of Extramarks NCERT Solutions, the student can score more in determinants and matrices.
NCERT Solutions Class 12 Mathematics Chapter 4 Exercise & Answer Solutions
NCERT Solutions Class 12 Mathematics Chapter 4 Determinant is available for students to refer to on the Extramarks website. It contains step-by-step solutions with detailed explanations. The students can solve complex problems with the easiest and most time-saving methods. Referring to our study material, students can make their basics strong and easily solve advanced theorems.
Click on the below links to view exercise-specific questions and solutions for NCERT Solutions Class 12 Mathematics Chapter 4 Determinant.
In addition to NCERT solutions class 12 mathematics chapter 4, students can also access other chapters of class 4. Furthermore, Extramarks offers NCERT solutions for other classes, which can be accessed by clicking on the respective link.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT Solutions Class 10
- NCERT Solutions Class 11
NCERT Exemplar Class 12 Mathematics
The NCERT Exemplar Class 12 Mathematics covers the essential subject knowledge. Once the students clear all the necessary topics under determinants, they can start preparing with an exemplar. There is a lot of importance to the topic as it appears in the competitive exams. Students can start preparing for their first-term CBSE exam with the help of this exemplar. It provides a complete explanatory solution for students with good knowledge of the subject.
At Extramarks, our subject matter experts offer their best solution with a proper step-by-step explanation. The exemplar consists of all the six exercises, i.e., introduction, determinant, properties of determinants, area of a triangle, minors and cofactors. In addition, the NCERT Exemplar contains various questions, multiple-choice type questions, and long answer type questions.
Key Features of NCERT Solutions Class 12 Mathematics Chapter 4
Class 12 Mathematics Chapter 4 has some essential elements that are a part of competitive exams. The students will get a detailed explanation of the terms, definitions, rules, and properties of determinants. A basic understanding of these complex theories is essential for better understanding. Hence, NCERT Solutions Class 12 Mathematics Chapter 4 offers a precise solution for each example mentioned in the exercise.
Some of the key features of NCERT Solutions Class 12 Mathematics Chapter 4 include:
- The solutions cover the entire syllabus of CBSE Class 12 Mathematics Chapter 4 and help to provide a detailed explanation of all topics.
- The format of the NCERT Solutions is self-explanatory and clears all doubts a student may have while learning complex concepts.
- To score better in the examination and competitive entrance exams, students must grasp all the topics. Hence NCERT Solutions Class 12 Mathematics Chapter 4 consists of all important aspects of Determinants needed for the competitive entrance exam.
- The solution helps increase knowledge in main topics.