NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions for Class 12 Maths – Free PDF Download

Class 12 Maths Chapter 3 NCERT solutions are now available online in PDF format. One can find the proper answers of Matrices Class 12 here, which have been developed by accomplished mentors complimenting their dexterity. The Class 12 Maths Ch 3 NCERT solutions PDF is uploaded on the official website. Download the file and start solving it right away.

Chapter 3 – Matrices 

NCERT Solutions for Class 12 Maths Chapter 3

3.1 Introduction

In NCERT Class 12 Maths Chapter 3 PDF, students will explore concepts of matrices. The learners can clearly understand the necessary application of matrices in various branches of mathematics. This mathematical tool simplifies the work to a great extent as compared to other straight forward methods. The evolution of the concept of Matrices 12th is the result of an attempt to extract compact and simple techniques of solving systems of linear equations. In this chapter, students will be better acquainted with the basics of matrix and matrix algebra. The utility of matrices expands far beyond the representation of the coefficients in the linear equations system.

Electronic spreadsheet programs for personal computers use Matrix notation and operations.

These, in turn, are used in different areas of business and science like budgeting, sales projection, cost estimation, analyzing the results of an experiment, etc. Many physical operations, such as magnification and reflection through a plane can be presented mathematically with the help of matrices. They are also used in cryptography. Good knowledge of matrices is important in varied individual branches of sciences and also in genetics, economics, sociology, modern psychology and industrial management.

3.2 Matrix

In this section of the chapter,  the fundamental principles of matrices are discussed. With the help of examples cited by established academicians, students can understand the whole concept. Get the proper definition of Matrix Class 12 and learn the order of a matrix considering only those matrices whose elements are real numbers or functions taking actual values. Students will get to know that the horizontal and vertical lines of entries in a matrix are called rows and columns respectively. This section also talks about the size of a matrix by the number of rows and columns it contains.

3.3 Types of Matrices

This part of the chapter delves into different types of matrices illustrated with various examples. It covers column matrix, row matrix, square matrix, diagonal matrix, scalar matrix, identity matrix and zero matrices. It also explores the equality of matrices accompanied with examples and solutions. The questions that have been provided will induce the sensibility of a learner to help them delve deeper into the aspects concerning the NCERT solution of Maths Class 12.

Exercise 3.1 Solutions: 10 Questions (5 Short Questions, 5 Long Questions).

3.4 Operations on Matrices

Matrix Class 12 NCERT Solutions introduces certain operations on matrices, namely, the addition of matrices, multiplication of a matrix by a scalar, differences and multiplication of matrices. Highlighting properties of matrix addition, scalar multiplication of a matrix, multiplication of matrices, etc., students can get a profound understanding of how matrices operate.

Exercise 3.2 Solutions: 22 Questions (3 Short Questions, 19 Long Questions).

3.5. Transpose of a Matrix

This section will focus on transposing a matrix and unique types of matrices such as symmetric and skew-symmetric matrices. It will establish the foundations of the transpose of the matrix with compelling examples and properties. This chapter engraves the basics with the help of illustrated examples and solutions.

3.6 Symmetric and Skew Symmetric Matrices

In this section, the chapter will assist in learning symmetric and skew-symmetric matrices. One can also comprehend the difference between a symmetric matrix and a skew-symmetric matrix. It is imperative to know about the transpose of a matrix and how to find it. Moreover, it is essential to remember all the parts of Chapter 3 that have been covered up until now. This section also explores theorems proving the nature of the symmetric matrix and skew-symmetric matrix.

Exercise 3.3 Solutions: 12 Questions (4 Short Questions, 8 Long Questions).

3.7 Elementary Operation (Transformation) of a Matrix

Above section of the chapter explains the six operations (transformations) on a matrix, three of which are due to rows and three due to columns. These are known as elementary operations or changes.

3.8 Invertible Matrices

Learn the properties of invertible matrices. This chapter highlights the process of finding a matrix's inverse is known as matrix inversion. It is essential to know that not all matrices are invertible. For a matrix to be invertible, it must be able to be multiplied by its inverse. Furthermore, one can learn how to invert a matrix by elementary operations, shaping a better idea with diverse examples.

Exercise 3.4 Solutions: 18 Questions (18 Short Questions)

Key Features of NCERT Solutions for Class 12 Maths Chapter 3

The chapter should be revised thoroughly to attain good marks in the exam. If a student adheres to the Matrices Class 12 NCERT solutions that have been developed by the experts, then they will learn the foundational base and the core concepts of the topic. The key features are provided as follows:

• Matrices Class 12 Solutions are crafted elaborately to assist students in the most uncomplicated fashion, easy to study and learn the chapter.

• With the Matrices Class 12 answers, students will be able to implant solid principles required to solve the exercises much quicker.

• Class 12 Maths NCERT Solutions Chapter 3 will always help any student facing doubts to clear them and understand promptly.

• Students should follow the instructions provided in the solutions that will help them attain more marks.