Notes from Toppers

System of Linear Equations - Detailed Notes


1. Types of Linear Equations

  • Read about the different types of linear equations mentioned in NCERT Class 11 Mathematics, Chapter 3:
    • Consistent Systems
    • Inconsistent Systems
    • Dependent Systems

References:

  • NCERT Class 11 Mathematics, Chapter 3, Section 3.2

2. Solving Systems of Linear Equations

  • Study various methods for solving linear equations, covered in NCERT Class 11 Mathematics, Chapter 3, Section 3.3:
  • Graphical Method
  • NCERT Class 11 Mathematics, Chapter 3, Section 3.3.1
  • Substitution Method
  • NCERT Class 11 Mathematics, Chapter 3, Section 3.3.2
  • NCERT Class 12 Mathematics, Chapter 4, Section 4.3.2
  • Elimination Method (Gaussian Elimination)
  • NCERT Class 11 Mathematics, Chapter 3, Section 3.3.3
  • Matrix Methods
    • Cramer’s Rule
    • NCERT Class 12 Mathematics, Chapter 4, Section 4.4
    • Matrix Inversion
    • NCERT Class 12 Mathematics, Chapter 4, Section 4.5

3. Matrix Algebra

  • Refer to NCERT Class 12 Mathematics, Chapter 4 for concepts related to Matrix Algebra:
  • Matrices and their Properties
  • Determinants and their Properties
  • Matrix Operations
  • Addition
  • Subtraction
  • Multiplication

4. Rank of a Matrix

  • Understand the concept of the rank of a matrix, covered in NCERT Class 12 Mathematics, Chapter 4, Section 4.6.

5. Homogeneous and Non-Homogeneous Systems

  • Learn about the differences between homogeneous and non-homogeneous systems, discussed in NCERT Class 12 Mathematics, Chapter 4, Section 4.3.1.
  • Study methods for solving both types of systems.

6. Applications of Linear Equations

  • Explore various applications of linear equations in fields such as physics, engineering, economics, and more.
  • Refer to relevant sections in NCERT Class 11 and Class 12 Mathematics textbooks, as well as additional reference materials.

7. Systems with Infinite Solutions

  • Study cases where systems of linear equations have infinitely many solutions, as mentioned in NCERT Class 12 Mathematics, Chapter 4, Section 4.3.3.
  • Understand the geometric interpretation of such systems.

8. Applications in Real-Life Problems

  • Practice solving real-life problems involving systems of linear equations. Refer to textbooks, study material, and online resources for examples and practice questions.

9. Word Problems

  • Solve word problems requiring you to set up and solve systems of linear equations. Look for word problems in NCERT textbooks, previous years’ question papers, and mock test series.