NCERT Solutions for Class 12 Maths Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 3: NCERT Solutions for Class 12 Maths Chapter 3, Matrices, are thoughtfully prepared by expert teachers to facilitate a thorough grasp of concepts from the NCERT textbook. These solutions are designed to make students comfortable and confident in addressing NCERT questions, aiming for maximum marks.

CBSE Class 12 Maths Syllabus

NCERT Solutions for Class 12 Maths Chapter 3 Overview

NCERT Solutions for Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths Chapter 3 Matrices (Properties and Formulas)

• An ordered rectangular array of numbers or functions is called a matrix.
• A matrix which has m rows and n columns is called a matrix of order m × n.
• [aij]m×1 is a column matrix.
• [aij]1×n is a row matrix.
• An m × n matrix is a square matrix if m=n.
• A = [aij]m×m is a diagonal matrix if aij=0, when i≠j.
• A = [aij]n×n is a scalar matrix if aij=0, when i≠j, aij=k (k is some constant), when i=j.
• A = [aij]n×n is an identity matrix if aij=1, when i=j, aij=0, when i≠j.
• A zero matrix has all its elements as zero.
• A = [aij] = [bij] = B if (i)A and B of the same order, (ii) aij = bij for all possible values of i and j.
• kA = k[aij]m×n = [k(aij)m×n]
• -A = (-1) A
• A – B = A + (-1) B
• A + B = B + A
• (A + B) + C = A + (B + C),  where A, B and C are of the same order.
• k (A + B) = kA + kB, where A and B are of the same order, k is constant.
• (k + l) A = kA + lA, where k and l are constant.

NCERT Solutions for Class 12 Maths Chapter 2

NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercises

Benefits of NCERT Solutions for Class 12 Maths Chapter 3

1. Concept Clarity: The solutions provide clear explanations of matrix-related concepts, ensuring students grasp the fundamental principles with clarity. This clarity is essential for building a strong foundation in the topic.
2. Step-by-Step Solutions: NCERT Solutions offer step-by-step solutions for each exercise and problem, guiding students through the logical sequence of solving matrix-related questions. This approach aids in understanding the process and logic behind each solution.
3. Exam Preparation: By practising with NCERT Solutions, students become well-acquainted with the question patterns that may appear in Class 12 exams. This familiarity enhances their preparedness and confidence during examinations.
4. Self-assessment: The solutions enable students to independently assess their understanding of matrix-related concepts. By comparing their solutions with the provided answers, students can identify areas of strength and weakness, allowing for targeted revision.
5. Problem-solving Skills: NCERT Solutions aid in the development of problem-solving skills. The stepwise approach demonstrated in the solutions assists students in mastering effective techniques for solving matrix problems.
6. Application of Concepts: The solutions illustrate practical applications of matrices, demonstrating how these mathematical tools are used to solve real-world problems. This application-oriented approach enhances students' understanding of the relevance of matrices in various fields.
7. Resource for Homework and Assignments: NCERT Solutions serve as a valuable resource for completing homework and assignments related to matrices. Students can refer to these solutions to verify their answers and ensure the accuracy of their work.
8. Consistency in Syllabus: The solutions adhere to the NCERT curriculum, ensuring that students cover all the topics prescribed for Class 12 Maths. This consistency is crucial for students appearing in board exams, as questions are based on the prescribed syllabus.
9. Structured Learning: NCERT Solutions provide a structured learning experience. Students can follow a logical progression of concepts, making it easier to understand the complexities of matrices.
10. Accessible and Free: NCERT Solutions are widely accessible and available for free, making them an inclusive resource for students across different backgrounds. This accessibility promotes equitable learning opportunities.
11. Preparation for Competitive Exams: Understanding matrices is essential not only for board exams but also for various competitive exams. NCERT Solutions equip students with the necessary skills and knowledge for tackling advanced mathematical problems.

How to Prepare With NCERT Solutions for Class 12 Maths Chapter 3

1. Understand the Basics: Begin by understanding the basic concepts of matrices. Familiarise yourself with the definitions, types of matrices, and fundamental operations.
2. Read NCERT Solutions: Go through the NCERT Solutions for class 12 maths Chapter 3. Read the solutions carefully to understand the step-by-step process of solving different types of matrix problems.
3. Practice Regularly: Practise solving matrix problems regularly. The more you practise, the more comfortable you become with different types of questions related to matrices. Consistent practice is key to mastering the chapter.
4. Self-assessment: Attempt exercises independently before referring to the solutions. After completing each problem, compare your solution with the provided answers. Identify areas where you made mistakes or need further clarification.
5. Review Mistakes: If you make mistakes, review them carefully. Understand the errors and learn from them. This process helps in avoiding similar mistakes in future practice and exams.
6. Explore Additional Resources: Supplement your preparation with additional resources like reference books, online tutorials, and practice quizzes. This can provide alternative perspectives and deepen your understanding of matrix-related concepts.
7. Utilise Online Platforms: Take advantage of online platforms that offer interactive learning resources and practice quizzes related to matrices. These platforms can provide additional exercises to reinforce your knowledge.
8. Group Study: Consider group study sessions with classmates. Discussing concepts with peers can offer different insights, clarify doubts, and expose you to varied problem-solving approaches.
9. Create a Revision Plan: Plan your revision systematically. Allocate time for regular revisions to reinforce your learning and ensure that you retain the concepts for a longer duration.
10. Seek Guidance: If you encounter challenges or have doubts, don't hesitate to seek guidance from your teachers, classmates, or online forums. Clearing doubts promptly is essential for a strong foundation.
11. Mock Tests: Take mock tests specifically focusing on matrices. Simulate exam conditions to enhance your time management and problem-solving skills.
12. Stay Consistent: Consistency is crucial for success. Set a regular study routine, and stay committed to your preparation plan. Consistent effort over time yields better results.