# NCERT Solutions for Class 12 Maths Chapter 3 Matrices

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NCERT Solutions for Class 12 Maths Chapter-3 Matrices

In this chapter, we will learn about matrices and its properties. Matrices is an important and powerful tool in mathematics. The Important topics that we are going to discuss in this chapter are a matrix, order of a matrix, types of matrices, equality of matrices, operations like addition multiplication on matrices, symmetric and skew-symmetric matrices etc. In chapter Matrices, there are 4 exercises with 62 questions. The NCERT Solutions for Class 12 Maths Chapter-3 Matrices are prepared by maths experts for the students to clear their doubts.

## What are matrices?

Matrix is a mode of representing data to ease calculation. And it is one of the most important tools of mathematics because matrices simplify our work to a great extent when we compared with other straight forward methods. Matrices are used as a representation of the coefficients in the system of linear equations, electronic spreadsheet programs, also used in business and science. For the students to understand NCERT Class 12 Maths Chapter 3 Matrices in a better way total 28 solved examples are given and also for more practice this topic at the end of the chapter 15 questions are given in the miscellaneous exercise.

## Topics and sub-topics of NCERT Grade 12 Maths Chapter-3 Matrices

3.1 Introduction

3.2 Matrix

3.2.1 Order of a matrix

3.3 Types of Matrices

3.3.1 Equality of matrices

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

3.5. Transpose of a Matrix

3.5.1 Properties of the transpose of the matrices

3.6 Symmetric and Skew-Symmetric Matrices

3.7 Elementary Operation (Transformation) of a Matrix

3.8 Invertible Matrices

3.8.1 Inverse of a matrix by elementary operations

Some example are-

Que.1 If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Solution-

'A'  matrix has 24 elements.

The possible orders are :

$1\times 24,24\times 1,2\times 12,12\times 2,3\times 8,8\times 3,4\times 6 \, \, and\, \, 6\times 4$.

If it has 13 elements, then possible orders are :

$1\times 13\, \, \, and \, \, \, \, 13\times 1$.

Que.2 If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Solution-

'A'  matrix has 18 elements.

The possible orders are as given below

$1\times 18,18\times 1,2\times 9,9\times 2,3\times 6\, \, \, and\, \, \, \, 6\times 3$

If it has 5 elements, then possible orders are :

$1\times 5\, \, \, and \, \, \, \, 5\times 1$.

## NCERT Solutions for Class 12 Maths Chapter 3 Matrices- Solved Exercise Questions

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.1

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.2

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.3

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.4

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Miscellaneous

## NCERT Solutions for class 12- Maths

 Chapter 1 Relations and Functions Chapter 2 Inverse Trigonometric Functions Chapter 4 Determinants Chapter 5 Continuity and Differentiability Chapter 6 Application of Derivatives Chapter 7 Integrals Chapter 8 Application of Integrals Chapter 9 Differential Equations Chapter 10 Vector Algebra Chapter 11 Three Dimensional Geometry Chapter 12 Linear Programming Chapter 13 Probability

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