NCERT Solutions for Class 12 Maths Chapter 3 - Matrices
NCERT Solutions for Class 12 Maths Chapter-3 PDF is made available for download. The student can find the official PDF on the Vedantu’s website and download it from there. The Matrices Class 12 PDF relating to the complete solutions have been provided for Chapter 3 of Class 12 NCERT Maths. You can find everything related to Chapter 3 Maths Class 12 there. The Matrices Class 12 CBSE NCERT Solutions PDF download has been developed by esteemed academicians who are in the field for quite some time. In addition to this, if anyone faces any doubts concerning CH 3 Maths Class 12, they can go to the website and drop in their queries and download the Matrices Class 12 NCERT PDF version. The helping team will get back to the student in case of doubts and clear that off in a very efficient manner.
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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
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.
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.
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.
FAQs (Frequently Asked Questions)
Q1: What are the main topics and subtopics of the chapter Matrices?
Ans: Matrices are one of the easiest chapters in maths, which, when understood, would become fun to solve. The concepts are as follows: Applications, Matrices, Order of matrices, Types of matrices includes Column matrix, Row matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, Zero matrix and Equal matrix. You will also read about Operations of matrices which includes Addition of matrices, Subtraction of matrices and Multiplication of matrices.
The chapter also explains about various laws which are: Commutative law, Associative law, Distributive law, Existence of multiplicative identity and Cancellation law. You will also get an idea of Transpose of a matrix, Properties of transpose, Symmetric and skew matrices and Invertible matrices.
Q2: Give me a glimpse of the chapter Matrices.
Ans: Matrices are majorly rectangular arrays of numbers which are represented in rows and columns. Basically, matrices are used to perform various mathematical operations such as addition, multiplication, subtraction and division. Representing data related to population, infant mortality rate, etc. are some of the widely used areas where matrices are implemented to simplify the calculations and ease the representation of data.
Matrices have substantial use in plotting graphs, statistics and various scientific research purposes. The most common and popular application of matrices is in solving linear equations. Matrices are even used to represent the coefficients of a linear equation. Other than that, matrices even find application in 3D maths, where they are used to define the relationship between two coordinate spaces.
Q3: How do our solutions help you in scoring good marks in the examination?
Ans: Start solving easier problems and slowly move to the medium level and then to the complex level. After each and every topic try to solve the questions and check where you are lagging behind. Practice the weaker area of that particular concept as many times as you can. This also helps you in knowing your strength along with the weakness.
Maths is always a part of our life and it will also be used in our day to day life. The short-cut technique to score well in maths is to practice. Do not mug up the solutions, try to understand them and solve it in your own way and then check where you have gone wrong.
Q4. Why should we learn about Matrices in NCERT Solutions for Class 12 Maths Chapter 3?
Ans: Matrices are a powerful and essential tool in Mathematics. They are rectangular arrays of numbers represented in the form of rows and columns. It is used to perform several mathematical operations like addition, subtraction, multiplication, and division. It is widely used in various areas to simplify complex operations like plotting graphs, representing the population, statistics, and in various research papers. It also simplifies the method of solving complex linear equations.
Q5. How many exercises are there in the Matrix?
Ans: There are four exercises and one miscellaneous exercise in the chapter Matrix. You can refer to the Maths Solutions for Class 12 by Vedantu, where you will find the detailed solution of every question in your Maths book. The solutions are explained in a simple and detailed manner and will clear your doubts. It also includes tips and important points that will help you score high in your exams.
Q6. Is Class 12 maths tough?
Ans: No, Class 12 Maths is not tough. You can score high by regular practice and strong concepts. Solve every question in your NCERT Maths book, including the solved questions. Refer to Vedantu’s Maths Solution for Class 12. It focuses on strengthening your concepts so that you can solve a variety of questions. Practice some questions daily to improve your solving skills. You can refer to Vedantu’s Revision Class 12 Notes which includes all the important concepts and formulas compiled in one place.
Q7. What are Matrices in Maths Class 12?
Ans: Matrices are rectangular arrays where data is represented in the form of rows and columns. It is a very easy and scoring topic. This chapter includes:
Types of Matrices
Operations on Matrices
Transpose of Matrices
Symmetric and Skew-symmetric Matrices
Elementary Operations (Transformation) on Matrices
These topics are explained in easy language so that the students can score high. You can practice a variety of questions in this chapter since it is relatively easier.
Q8. Why should you refer to Vedantu’s Solutions for Class 12 Maths?
Ans: Vedantu’s Solutions for Class 12 Maths are prepared by experienced subject-matter experts and include answers to every question in your NCERT Maths book. It includes all the important formulas, concepts, and theorems that are very important from the exam point of view. The solutions are updated according to the latest guidelines of the CBSE board. This is also very useful for revision before your exam. It includes step-wise solutions that will help you to understand the concepts well. The solution PDFs and other study materials such as important questions and revision notes can also be downloaded from the Vedantu app as well for free of cost.