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JEE Main - Matrices and Determinants Notes (Free PDF Download)

Last updated date: 16th May 2024
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Download JEE Main Matrices and Determinants Notes with Important Topics and Prepare Efficiently

Prepare effectively for JEE Main by downloading the Matrices and Determinants Notes with important topics. These notes, Prepared by our master teachers, simplify complex concepts, highlight key points, and provide important topics. You can download them for free from our website. These comprehensive revision notes condense the essential information you need to know, making your preparation efficient. As you delve into the topics covered, you'll enhance your understanding and be well-prepared for the exam. Get ready to excel in JEE Main with these valuable resources at your disposal. 


JEE Main Revision Notes


Text, Images, Videos and PDF


JEE Main

Chapter Name:

Matrices and Determinants

Academic Session:



English Medium



Available Material:

Chapter-wise Notes with PDF

The chapter Matrices and Determinants discusses fundamental concepts in linear algebra. Matrices are arrays of numbers organized in rows and columns, used to represent linear transformations and solve systems of equations. Determinants provide information about the properties of matrices, such as invertibility and consistency, which are some of the key topics for the JEE Main exams. Looking at the old JEE Main question papers, you'll see 2 questions were from this chapter. Take a look at the  table for more details.

Year Wise Weightage of Questions: JEE Main Matrices and Determinants

Sl. No.


Average No. Of Questions Asked

Marks per Question

Total Marks





















Over the last five years of JEE Main exams, about 2 questions were asked from Matrices and Determinants. Now you know how much weightage you have to give to this chapter. The teachers put in dedicated efforts to ensure the Matrices and Determinants notes align perfectly with the JEE Main syllabus. Get ready to do well – get your Matrices and Determinants Notes and shine in JEE Main 2025!

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JEE Main 2025: Must-Revise Topics in Matrices and Determinants

Let's focus on the key topics you should review in Matrices and Determinants. These important topics can make a real difference in your preparation. Mastering them will give you a strong edge in the upcoming exam. Let's dive into the must-revise topics to help you shine in JEE Main 2025.


  • Matrix Operations

  • Matrix Multiplication

  • Transpose of a Matrix

  • Types of Matrices (Identity, Zero, Diagonal, Symmetric, etc.)

  • Inverse of a Matrix

  • Rank of a Matrix

  • Row and Column Operations

  • Adjoint and Cofactor

  • System of Linear Equations


  • Determinant of a Matrix

  • Properties of Determinants

  • Cramer's Rule

  • Minors and Cofactors

  • Expansion of Determinants

  • Vandermonde Determinant

  • Solving Equations using Determinants

  • Area and Volume using Determinants

Maths Notes for JEE Main 2025 Chapters: Links Available

Make your JEE Main Maths studying for 2025 even better using our notes organized by chapter. FindThe links in the table below for easy access.

How Matrices and Determinants Can Shape Your JEE Main 2025 Journey?

What are Matrices and Determinants?

  • Imagine organizing numbers in a grid – that's a matrix! It's a handy way to crunch data, solve equations, and even transform shapes.

  • Determinants, on the other hand, are like magical numbers that reveal whether a matrix has special properties.

The Matrix Maze: A Fun Adventure!

  • Navigate through rows and columns, adding, subtracting, and multiplying numbers – that's matrix arithmetic!

  • Need to scale, rotate, or stretch? Matrices got you covered with transformations.

Unlocking Equations:

  • Ever wondered how to solve systems of linear equations? Matrices swoop into the rescue with elegant solutions.

  • Craving some 3D graphics magic? Matrices play a pivotal role in computer graphics and engineering.

Row Operations: Matrix Makeovers:

  • Just like rearranging furniture in a room, row operations let us transform matrices. We can swap, scale, and add rows to create new matrix worlds!

  • It's like solving puzzles – you tweak one row, and the whole matrix story changes!

Enter the Determinants: The Deciding Factors!

  • Determinants determine whether a matrix has an inverse – like checking if a secret door can be opened!

  • When the determinant is zero, things get interesting! Explore singular matrices and unique solutions.

Cramer's Rule: Solving the Mystery:

  • Cramer's Rule is like Sherlock Holmes – it solves the mystery of solving systems of linear equations using determinants.

  • Uncover the power of determinants to solve real-world problems, from electrical circuits to economic models.

Eigenvectors and Eigenvalues: The Superheroes:

  • Eigenvectors and eigenvalues are the superheroes of matrices. They reveal the secret transformations matrices have on special vectors.

  • It's like discovering hidden powers in everyday objects – you'll be amazed by their applications in physics and computer graphics!

Real-World Connections: Bringing Matrices to Life:

  • Matrices and determinants aren't just abstract concepts. They're the gears behind modern technology, from image processing to cryptography.

  • Dive into real-world examples – crack codes, create stunning visuals, and understand complex systems with the magic of matrices!

Strategies for JEE Main Success:

  • Master matrix multiplication and manipulation – a go-to skill for solving complex problems.

  • Understand how determinants shape solutions in linear algebra and geometry.

  • Practice solving matrices and determinants problems to build confidence.

Real-World Magic:

  • Matrices rule the world of data analysis, machine learning, and cryptography – think of them as secret codes and keys.

  • Determinants pop up in physics, engineering, and economics, making them vital tools for understanding real-world phenomena.

Tips for a Joyful Journey:

  • Visualize matrices as grids that organize numbers – it's like arranging puzzle pieces!

  • Embrace determinants as magical keys that unlock insights hidden within matrices.

  • Practice matrix multiplication with interactive exercises for a hands-on experience.

Step into the Matrix: Ready to Rock JEE Main!

  • Use matrices to simplify complicated problems, ace linear equations, and understand transformations.

  • Let determinants be your allies in discovering special matrix properties and solving intriguing puzzles.

Embrace the journey into the captivating world of Matrices and Determinants, where grids turn into tools for solving mysteries, equations, and real-world challenges. These mathematical wonders are your ticket to confidently conquering JEE Main and beyond!

Formulaic Support: Boosting Understanding with Revision Note Integration

If you want to learn well, you can use a clever plan by merging formulas and revision notes. Formulas are like short explanations of important concepts. You get a complete learning method when you use them with detailed revision notes. Revision notes build a strong foundation, and formulas help you grasp concepts and solve problems.This combination makes tough things simpler and improves memory. Following this approach can enhance your understanding and help you perform well in your studies.

Download Vedantu's JEE Main Maths Formulas for FREE. Blend it with JEE Main Notes, and you'll notice positive score changes.

Next Steps: Further Resources for JEE Main 2025 Matrices and Determinants

Ready to take your JEE Main 2025 Matrices and Determinants preparation up a notch? Delve into these crucial resources:

  • Practice Papers: Hone your skills with targeted practice.

  • MockTests: Simulate exam conditions and boost your confidence.

  • Sample Papers: Familiarize yourself with the question patterns.

  • Previous Year Question Papers (PYQPs): Gain insights into the exam's structure and trends.

Combine these resources to refine your understanding and exam-taking abilities. Elevate your performance for JEE Main 2025!

Here are the links for the additional resources of JEE Main 2025:

Get Ahead in Your Exams with Vedantu’s JEE Main Notes

In your journey towards exam success, Vedantu's Matrices and Determinants JEE Main Notes are your trusted companion. Our unique approach, combining expert guidance and student-friendly resources, sets us apart. With comprehensive revision notes at your fingertips, complex concepts become clear and preparation becomes more efficient. What's more, These valuable resources are available to you as FREE PDFs. Trust Vedantu to help you stride confidently towards acing your exams. Elevate your learning experience, simplify your studies, and embrace excellence with Vedantu.

FAQs on JEE Main - Matrices and Determinants Notes (Free PDF Download)

1. What are the Matrices and Determinants in the context of JEE Main 2025?

In the context of JEE Main 20245, matrices refer to arrays of numbers arranged in rows and columns. Determinants are mathematical values associated with square matrices, used to solve equations, compute inverses, and understand linear transformations. These concepts are essential in mathematics and physics, and may appear as topics in the JEE Main 2025 examination.

2. How can I apply the Matrices and Determinants to solve JEE Main problems?

To tackle JEE Main problems involving matrices and determinants, follow these steps:

  • Understand basic concepts and properties.

  • Practice various types of problems to build familiarity.

  • Apply matrix operations for transformations and solving linear equations.

  • Use determinants for solving systems of equations and testing invertibility.

  • Review key theorems and practice timed mock tests for efficiency.

3. What are some strategies to effectively use Matrices and Determinants notes for JEE Main 2025 preparation?

StrategiesTo effectively use Matrices and Determinants notes for JEE Main 2025 preparation are:

  • Regularly review your notes and reinforce concepts.

  • Practice solving various types of problems to build problem-solving skills.

  • Focus on understanding the applications and implications of each law.

  • RelateTheoretical concepts to real-world scenarios mentioned in your notes.

4. Which are the most important topics of Matrices and Determinants Notes for JEE Main 2025?

The important topics covered in the Matrices and Determinants Notes for JEE Main 2025 include:


  • Matrix Operations: Addition, Subtraction, Multiplication.

  • Transpose and Inverse.

  • Types of Matrices: Identity, Zero, Diagonal, Symmetric, Skew-Symmetric.

  • Rank of a Matrix.

  • System of Linear Equations and Cramer's Rule.

  • Row Echelon Form and Reduced Row Echelon Form.

  • Linear Independence and Dependence.


  • Determinant of 2x2 and 3x3 matrices.

  • Properties of Determinants: Multiplicative Property, Transpose Property.

  • Cramer's Rule for Solving Linear Equations.

  • Area and Volume using Determinants.

  • Properties of Rank and Nullity.

Eigenvalues and Eigenvectors (Optional but useful):

  • Eigenvalues and Eigenvectors of a Matrix.

  • Diagonalization of Matrices.

  • Characteristic Polynomial.

5. Which is the easiest topic of JEE Main 2025 Matrices and Determinants Notes?

The concept of basic matrix operations, such as addition, subtraction, and scalar multiplication, is often considered one of the easier topics in the Matrices and Determinants section of JEE Main 2025. Understanding these fundamental operations lays the groundwork for more advanced matrix concepts.

6. Where can I find additional resources to supplement JEE Main 2025 Matrices and Determinants Notes?

You can discover supplementary resources to enhance JEE Main 2025 Matrices and Determinants preparation through Vedantu’s website. These resources offer practice papers, video lectures, interactive quizzes, and discussions that complement your JEE Main notes, enriching your understanding and exam readiness.

7. What is the weightage of Matrices and Determinants Notes for JEE Main 2025?

The weightage of Matrices and Determinants Notes for JEE Main is around 8 marks. This chapter is of high weightage and maximum marks questions are asked, therefore, students should not ignore these chapters and revise every concept thoroughly.

8. How much time is required to prepare for JEE Main 2025 Matrices and Determinants Notes?

The time required to prepare for JEE Main 2025 Matrices and Determinants Notes varies based on your familiarity with the concepts, study habits, and practice efforts. On average, a few weeks of consistent study, including active reading, problem-solving, and revision, should provide a solid foundation. However, it's essential to tailor your study plan to your learning pace and commit sufficient time for comprehensive understanding and practice.