NCERT Class 12 Mathematics Mathematics Part-I: Chapter 3 — MATHEMATICS
This chapter introduces the concept of matrices, a powerful mathematical tool used in various fields. Matrices simplify complex calculations, especially for solving systems of linear equations. They are utilized in spreadsheets for business and science applications like budgeting and sales projection, and in representing physical operations such as magnification and rotation. Matrices also find applications in cryptography, genetics, economics, sociology, psychology, and industrial management. The chapter aims to familiarize students with the fundamentals of matrices and matrix algebra, providing a foundation for further study in mathematics and its applications.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 12 |
| Subject | Mathematics |
| Book | Mathematics Part-I |
| Chapter | Chapter 3 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 432 |
Learning outcomes
- Understand the definition and basic representation of matrices.
- Recognize the utility of matrices in solving real-world problems.
- Appreciate the historical development and diverse applications of matrices.
Vocabulary
| Word | Meaning |
|---|---|
| Matrices | A rectangular array of numbers, symbols, or expressions, arranged in rows and columns. |
| Linear equations | Equations in which each term is either a constant or the product of a constant and a single variable. |
| Matrix algebra | The branch of mathematics dealing with the properties and operations of matrices. |
| Cryptography | The practice and study of techniques for secure communication in the presence of third parties. |
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Practice questions
- How can the information about Radha having 15 notebooks and 6 pens be represented using a matrix? Answer: It can be represented as [15 6].
- What is a primary historical motivation for the development of matrices? Answer: To obtain compact and simple methods for solving systems of linear equations.
- Name two areas outside of pure mathematics where matrices are used. Answer: Examples include business (budgeting, sales projection), science (analyzing experimental results), genetics, economics, sociology, psychology, industrial management, and cryptography.
Practice MCQs
Q1. Matrices are primarily introduced as a tool to simplify which type of mathematical problem?
Explanation: The text explicitly states that the evolution of the concept of matrices is a result of an attempt to obtain compact and simple methods of solving systems of linear equations.
Q2. Which of the following is NOT mentioned as an application area for matrices?
Explanation: Musical composition is not mentioned in the provided text as an application area for matrices. The text lists business, science, genetics, economics, sociology, psychology, industrial management, and cryptography.
Q3. The arrangement of numbers in rows and columns to represent data is called a:
Explanation: The text defines a matrix as a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, used to represent information.
Q4. According to the text, matrices are useful in electronic spreadsheet programs for:
Explanation: The text mentions that matrix notation and operations are used in electronic spreadsheet programs for personal computer applications such as budgeting, sales projection, and cost estimation.
Q5. The quote at the beginning of the chapter is attributed to:
Explanation: The quote 'The essence of Mathematics lies in its freedom' is attributed to CANTOR.
Frequently asked questions
What is a matrix in mathematics?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns, used to represent data or solve mathematical problems.
Why are matrices important in mathematics?
Matrices are powerful tools that simplify complex calculations, particularly in solving systems of linear equations, and have wide applications in science, business, and technology.
What historical problem led to the development of matrices?
The need for compact and simple methods to solve systems of linear equations was a primary driver for the development of matrix concepts.
In which fields are matrices used besides mathematics?
Matrices are used in business (budgeting, sales projection), science (analyzing experiments), genetics, economics, sociology, psychology, industrial management, and cryptography.
How are matrices used in computer applications?
Matrix notation and operations are used in electronic spreadsheet programs for tasks like budgeting, sales projection, and cost estimation.
Related resources
Important topics
Topics covered
NCERT Class 12 Mathematics — Mathematics Part-I — Chapter 3 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.