Table of Contents

**NCERT Exemplar solutions chapter 3 Matrices**

Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 3 Matrices, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 12 maths chapter 3 matrices provide useful solutions for improving conceptual knowledge and help in entrance examinations like **JEE mains** and** NEET.**

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12 pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

These NCERT Exemplar Solutions includes the following topics and subtopics. Students should practise problems on these topics to get ready for the term – I exam with the help of Infinite lean.

**3.1 Introduction**

In this chapter, students came to know the fundamentals of matrix and matrix algebra and how matrices are associated with different fields.

**3.2 Matrix**

**3.2.1 Order of a matrix**

This portion, it explains clearly with an easy example of how the elements are arranged to form a matrix and how its order can be defined.

**3.3 Types of matrices**

3.3.1 Equality of matrices

We came to know about different types of matrices in this section such as column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, and zero matrices. Also, the equality of matrices is explained with examples.

**3.4 Operations on Matrices**

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

After this portion, students will came to know about certain operations on matrices, namely, the addition of matrices, multiplication of a matrix by a scalar, difference, multiplication of matrices, and respective properties.

**3.5 Transpose of a Matrix**

3.5.1 Properties of the transpose of the matrices

Transpose of a matrix and properties are well explained with examples. These examples also prove the properties of the transpose of a matrix.

**3.6 Symmetric and Skew Symmetric Matrices**

In this part, students will understand the definitions of symmetric and skew symmetric matrices, along with the related theorems and examples.

**3.7 Elementary Operation (Transformation) of a Matrix**

After going through this section, students will learn transformations on a matrix. There are total six operations, i.e. transformations on a matrix. Three are due to columns and three due to rows, which are known as elementary operations or transformations.

**3.8 Invertible Matrices**

3.8.1 Inverse of a matrix by elementary operations

Here, students will understand the necessary conditions for matrices to have the inverse of them. Also, it has been given that how to get an inverse matrix by performing elementary operations on the elements of a matrix.

: 10 Questions (7 Short Answers, 3 MCQs)

: 22 Questions (14 Long, 6 Short, 2 MCQs)

: 12 Questions (10 Short Answers, 2 MCQs)

: 18 Questions (4 Long, 13 Short, 1 MCQ)

: 15 Questions (7 Long, 5 Short, 3 MCQs)

The NCERT Exemplar Solutions to questions provided by infinite learn has covered all the below mentioned properties and formulas.

- An ordered rectangular array of numbers or functions is called a matrix.
- A matrix which 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.

**Frequently Asked Questions**

##### What are the main topics discussed in these NCERT Exemplar Solutions?

In Mathematics, matrices are one of the easiest chapters, they are easy to understand. Matrix, types of matrices, operations on matrices, transpose of a matrix, symmetric and skew symmetric matrices, elementary operation on matrix and invertible matrices are the main topics included in this chapter. These topics are discussed in easy language to help students score well in the first term exams irrespective of their intelligence quotient.

##### Why should we learn about matrices from NCERT Exemplar Solutions of this chapter?

Matrices represent rectangular arrays of numbers which are represented in rows and columns. Various mathematical operations like multiplication, addition, subtraction and division can be done using matrices. Representing the data related to infant mortality rate, population etc. are the widely used areas where matrices are used to simplify the complex data. The other known use of matrices are statistics, plotting graphs and various scientific research purposes. The method of solving difficult linear equations are also made easy using the matrices.

##### Do these NCERT Exemplar Solutions help you to score well in the term – I exam?

This chapter includes all the important topics based on the latest update of CBSE guidelines. Four exercises are provided in this chapter giving the students with numerous problems to solve independently. The solutions are made to boost the confidence in the minds of students before appearing for the term I exams. These solutions are thus helpful to score well for the term 1 exam.

##### Why Opt for Infinity Learn?

In this chapter Infinity Learn provides videos, notes, NCERT textbook solutions, other practice book solutions and assignments that help you learn the concepts and to memorise the concepts for entrance exams and board exams. Most important, Infinity learn provide instant doubt support by subject experts.

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