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# NCERT Solutions for Class 12 Maths Chapter 3 – Matrices

Our NCERT Solutions for Class 12 Maths Chapter 3 – Matrices is the best source of learning effectively for CBSE Board exams. Here, you will learn various interesting topics such as order of a matrix, types of matrices which includes column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, unit or identity matrix, zero or null matrix and equality of matrix. This chapter of NCERT Solutions also covers operations on Matrices like addition and subtraction of matrices, properties of addition of matrices and multiplication of a matrix by scalar number and multiplication of matrices.  Our NCERT Solutions cover all topics and sub-topics of the chapter in a step by step manner to help you learn even the most difficult topics easily.

NCERT CBSE Class 12 Maths Chapter 3 comprises 4 all-inclusive exercises and 1 miscellaneous exercise that consist of more than 50 questions that touch all parts of the chapter. Our NCERT Solutions answers all questions from all exercises in detail, in an easy to understand and structured manner to incite effective learning and help you become thorough with the chapter.

Our NCERT Solutions help you keep your concepts clear and ensure that you have a proper conceptual foundation. The solutions provided by us are relevant and highly informative and of the finest quality.  They are just what you need to perform exceptionally well in your Class 12 board exams and various competitive exams.

## CBSE NCERT Class 12 Maths Chapter 3: Important Topics

Our NCERT Solutions for Class 12 Maths Chapter 3 – Matrices not only gives you an overall picture of the chapter but also gives you an in-depth understanding of all concepts of the chapter. Some of the topics covered in this chapter have been discussed below.

• Introduction

This segment of CBSE NCERT Class 12 Maths Chapter 3 – Matrices introduces you to a matrix, which is an ordered rectangular array of functions and numbers. Elements or entries of the matrix are these functions or numbers.

• Order of a Matrix

This section of the chapter will teach you about the order of a matrix. If a matrix has n columns and m rows, as per the order of a matrix, it will be as m x n. If the matrix is to be represented in order of m x n, then it has mn elements.

• Types of Matrices

This part of NCERT Class 12 Maths Chapter 3 explains various forms of matrices. Some of them are as follows.

1. Column Matrix:
This part explains to you how the matrix is represented in column form or in one single matrix column.
For Example

A = [aij]m x 1  is a column matrix of order m x 1
2. Row Matrix:
This part explains to you how the matrix is represented in row form or one single matrix row.

For Example: [ 2  3 1 ]
A = [aij]1 x n  is a row matrix of order 1 x n

3. Square Matrix:
This section of the chapter teaches you that, if you have an equal number of columns and rows in a matrix, then it is called a square matrix.

For Example:
4. Diagonal Matrix:
This section of the chapter teaches you how to represent diagonal matrices and the similarities of diagonal and square matrices.
For Example:

5. Scalar Matrix:
This segment of NCERT Solutions for Class 12th Maths Chapter 3 – Matrices, teaches you that the elements whose diagonal numbers are the same will be considered as scalar matrices.
For Example:
6. Unit or Identity Matrix:
This section of Class 12 Maths Matrices, discusses the identity or unit matrix. Here, you will understand that if all the diagonal numbers are represented with 1 and the non-diagonal numbers are  0 it will be considered as unit or identity matrices.
For Example:

•  Zero or Null Matrix:

This section of CBSE NCERT Class 12 Maths book, will discuss the zero or null matrix. If all the numbers or elements present in a matrix are ‘0’ then it will be considered as zero or null matrix. For Example:

The later part of the chapter throws light on equality of matrices, operations on matrices, Addition of and subtraction of matrices, Multiplication of a matrix by a scalar number, Properties of the addition of matrices, Properties of scalar multiplication of a matrix, Multiplication of matrices, Properties of multiplication of matrices, Transpose of a Matrix, Properties of the transpose of the matrices, Symmetric and Skew-Symmetric Matrices, Elementary Operation (Transformation) of a Matrix, Invertible Matrices and Inverse of a matrix by elementary operations.

## NCERT CBSE Class 12 Maths Chapter 3 Exercise Questions

There are a total of 4 exercises along with one miscellaneous exercise at the end of the chapter. NCERT Solutions for Chapter 3 – Matrices answer all questions of all exercises in a step by step manner. Below is a brief overview of the exercises.

Exercise 3.1:

• This exercise consists of 10 questions in total. In which, question 1, 2, 3 and 4 are based on an introduction to the matrix, which mainly focuses on the order of the matrix. In question 5, you will be given the elements, and you will have to construct a 3 x 4 matrix.
• 6 and 7 ask you to find the value of the given equations. The questions are based on the operations.
• Question 8 to 10 are multiple-choice questions. The questions are based on square matrices and equality of matrices.

Exercise 3.2

• This exercise consists of 22 questions in total. Question 1, 2 and 3 are based on the operations. In which you will have to solve the questions based on the indications mentioned. Matrices used in this are addition, subtraction and multiplication.
• Question 4 is based on operations of the matrix. In which you have to solve the question in both the ways by addition and subtraction. Question 5 and 6 are based on the subtraction of matrices.
• Question 7 to 12 are based on finding the equations. In these questions, you will be given the matrix in which the values are to be figured.
• In question 13 and 14, you’ll have to find if both the matrices are equal or not equal. These questions are based on the equality of the matrix.
• From question 15 to 18, you’ll have to derive the equation with the help of the matrix. The questions are based on the properties of the transpose of the matrices.
• Question 19 and 20 are scenario-based questions, in which multiplication of matrices concept is covered.
• Question 21 and 22 are multiple-choice questions. These questions are based on the order of the matrix.

Exercise 3.3:

• This exercise consists of 12 questions in total. In this, question 1 to 6 and 9 are based on the transpose of a Matrix and properties of it.
• Questions 7 to 10 are based on the symmetric and skew-symmetric concepts. These questions are to be solved in the same pattern with the help of transpose of a matrix.
• Questions 11 and 12 are multiple-choice questions. These questions are covered from the transpose and operations concepts.

Exercise 3.4:

• This exercise consists of 18 questions in total. Question 1 to 17 are based on the elementary transformations, in which you have to find the inverse of each of the matrices if they exist.
• Question 18 is a multiple-choice question. This question covers the inverse of a matrix by the elementary transformation.

Miscellaneous Exercises:

• Miscellaneous Exercise consists of 15 questions in total. Question 1, 2 and 3 are based on the identity matrix or unit matrix. Question 4 and 5 are based on skew matrices.
• Question 6 to 9 and 11 covers the operations of matrix topics. Question 10 is a scenario-based which is to be solved with the help of multiplication of matrices.
• Question 12 is based on the square matrix. Question 14 and 15 are multiple-choice questions. These two questions are based on symmetric or skew-symmetric and square matrices.

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

There are many upsides of learning and practising from our carefully drafted NCERT Solutions for Class 12 Maths Chapter 3-Matrices. Some of them have been given below.

• Our maths expert teachers have framed these solutions in an easy language to make your preparation effective, efficient and fast.
• Our NCERT solutions have been drafted meticulously on the basis of the latest and updated CBSE Class 12 Maths Syllabus.
• They cover a wide range of question types important from Class 12 board exam point of view.
• Our smart study techniques and learning shortcuts help you learn quickly and score more marks
• Our NCERT Solutions are well-structured, comprehensive, yet to the point.
• They have been designed to clear all your doubts and improve your retention rate.
• They have been solved using the best methods of solving the problems.
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