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.