# NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

NCERT Solutions for Class 12 Maths Chapter 3: Matrices are one of the fresh topics that work as a sunshine plot for the intricate Maths syllabus. Matrices Class 12 NCERT Solutions are created by expertise. These solutions assist students in comprehending the topics presented in the NCERT textbook for Matrices.

Well, we provide extensive solutions to every NCERT question, allowing students to feel at ease and secure in their ability to achieve the highest possible grade. Download and go through the NCERT Solutions for Class 12 Maths Chapter 3 PDF!

Table of Contents

## Download NCERT Solutions for Class 12 Maths Chapter 3: Matrices PDF

Our Maths specialists solve Class 12 Maths NCERT Solutions in a step-by-step manner, following NCERT rules, to assist you in the Class 12 board exams. Download NCERT Solutions for Class 12 Maths Chapter 3 in your system and start our preparation for the finals.

### Access Matrix Class 12 NCERT Solutions

Class-12-Mathematics-Solutions-Chapter-3 pdf

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## What will you learn in Matrix Maths Class 12 NCERT Solutions?

Matrices are one of the most important and powerful tools in mathematics. This mathematical tool is now applied in genetics, economics, sociology, modern psychology, and industrial management, in addition to certain disciplines of science.

NCERT Solutions for Class 12 Chapter 3 cover the following concepts and subtopics. You can use Kopykitab’s Matrices Class 12 NCERT Solutions to practice problems on these topics and prepare for the exam.

### 3.1: Introduction

This chapter covers every single aspect of matrix algebra thus imparting students the basics of matrices and topics associated with the same.

### 3.2: Matrix

This section teaches students with minute details regarding the matrix and order of the matrix with easy examples for a thorough understanding of the chapter. It also teaches us the elemental arrangements to form a matrix and order and definitions.

### 3.3: Types of Matrices

This segment teaches us about the variations in the matrix such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices.

### 3.4: Operations of Matrices

This section covers-

3.4.1 Addition of matrices

3.4.2 Multiplication of a matrix by a scalar

3.4.3 Properties of matrix addition

3.4.4 Properties of scalar multiplication of a matrix

3.4.5 Multiplication of matrices

3.4.6 Properties of multiplication of matrices

### 3.5: Transpose of Matrix

This segment lets students a clear picture of the transpose matrix and properties of the same with examples to follows. The examples are given in the chapter help the reader to learn the minute details of the topic along with the transpose of a matrix.

### 3.6: Symmetric and Skew Symmetric matrices

This portion of the chapter clears the concept of  Symmetric and Skew symmetric matrices with definitions alongside associated formulas, examples, and theorems.

### 3.7: Elementary Operation(Transformation of a matrix)

This segment manages to impart the student with a sorted understanding of what is the transformation of the matrix. Amongst the processes three are due to columns and three due to rows. These are termed elementary operations or fundamental transformations.

### 3.8: Invertible Matrices

The segment teaches the various practical situations for matrices to inverse them. Here students will also get detailed knowledge about how to get an inverse matrix by performing elementary operations on the elements of the matrix.

#### Let us now check out the exercises covered in the NCERT Solutions for Class 12 Maths Chapter 3-

 Exercise 3.1 Solutions 10 Questions(7 short answers, 3 MCQs) Exercise 3.2 Solutions 22 Questions (14 Long, 6 Short, 2 MCQs) Exercise 3.3 solutions 12 Questions (10 Short Answers, 2 MCQs) Exercise 3.4 solutions 18 Questions (4 Long, 13 Short, 1 MCQ) Miscellaneous Exercise Solutions: 15 Questions (7 Long, 5 Short, 3 MCQs

## NCERT Solutions for Class 12 Maths Chapter 3- Matrices: Theorems and formulas Used

• An ordered rectangular array of numbers or functions is called a matrix.
• A matrix that has m rows and n columns is called a matrix of order m × n.
• [aij]m×1 is a column matrix.
• [aij]1×n is a row matrix.
• An m × n matrix is a square matrix if m=n.
• A = [aij]m×m is a diagonal matrix if aij=0, when i≠j.
• A = [aij]n×n is a scalar matrix if aij=0, when i≠j, aij=k (k is some constant), when i=j.
• A = [aij]n×n is an identity matrix if aij=1, when i=j, aij=0, when i≠j.
• A zero matrix has all its elements as zero.
• A = [aij] = [bij] = B if (i)A and B of the same order, (ii) aij = bij for all possible values of i and j.
• kA = k[aij]m×n = [k(aij)m×n]
• -A = (-1) A
• A – B = A + (-1) B
• A + B = B + A
• (A + B) + C = A + (B + C), where A, B and C are of the same order.
• k (A + B) = kA + kB, where A and B are of the same order, k is constant.
• (k + l) A = kA + lA, where k and l are constant.

## Benefits of NCERT Solutions for Class 12 Maths Chapter 3

The chapter is unquestionably great assistance to gear up your exam preparation. Let us look at the several important notions that support this ideology-

1. When you are studying Maths with Solutions for Class 12 Maths Chapter 3 – Matrices, your exam preparation is sure guided by some of the trustworthy platforms without any doubt.
2. The subject matter panel works in bringing out the best of the study content for your solid exam preparation.
3. NCERT Maths Chapter 3 Solutions would assist students in solidifying their understanding of Matrices topics.
4. The study material is styled and curated by professionals to impart what is best suited to the students.
5. After revising them, you would be able to focus better and achieve a higher grade.
6. These solutions will aid in the development of student confidence.
7. With the practice of each single sums given in the chapter, you are increasing your chances of scoring colorful marks for your finals which is great indeed.

Well, we have come down with all the necessary points that ensure your CBSE NCERT Solutions for Class 12 Maths Chapter 3 – Matrices well-grounded preparation. If you still face any queries with the topics make sure to ask us in the comment section below. We would be more than happy to help you out!

### How many exercises are there in Chapter 3 of the NCERT textbook for Class 12 Maths?

In total, there are four exercises in Chapter 3 of Class 12 Maths.

### Where can I get Maths Chapter 3 Class 12 NCERT solutions?

You can get NCERT Solutions for Class 12 Maths Chapter 3 from the above blog.

### Is NCERT Solutions Class 12 Maths Chapter 3 helpful?

Yes, the NCERT Chap-3 exercises are addressed by subject matter experts who have a thorough understanding of the key ideas and every step is described in easy-to-understand language.

### Can I receive an overview of the NCERT Solutions for Class 12 Maths Chapter 3 exercises?

Yes. Go through the above blog for an overview of the NCERT Solutions for Class 12 Maths Chapter 3 exercises.

### Are Matrices Class 12 NCERT Solutions enough for board examinations preparation?

Yes. Matrices Class 12 NCERT Solutions covers all the topics of a matrix which is sufficient for board examinations preparation.