L(caps)inear Algebra is one of the most fundamental and scoring subjects in the GATE exam. It covers concepts like vector spaces, basis, matrix algebra, eigenvalues, rank, and solutions of linear equations. Mastering these topics not only strengthens your mathematical foundation but also helps you solve problems faster and more accurately in the exam.
(toc)(Table of Content)
📘 GATE Linear Algebra Syllabus
Linear Algebra is one of the most important and high-scoring topics in the GATE Exam. It builds the foundation for advanced concepts and appears almost every year in the question paper. Let’s break down the official syllabus into simple parts:
Topics Covered
1. Vector Space
- Concept of vectors, addition, and scalar multiplication.
- Subspaces and properties
2. Basis & Dimension
- Basis of a vector space
- Dimension and change of basis
3. Linear Dependence & Independence
- Identifying dependent and independent vectors
- Applications in solving vector problems
4. Matrix Algebra
- Matrix operations (addition, multiplication, inverse, transpose)
- Special matrices (identity, diagonal, symmetric, orthogonal)
5. Eigenvalues & Eigenvectors
- Characteristic equation
- Diagonalization and applications
6. Rank of a Matrix
- Row rank & column rank
- Rank–nullity theorem
7. System of Linear Equations
- Existence of solutions
- Uniqueness of solutions using rank
📌 Why It’s Important for GATE?
- Linear Algebra questions are conceptual + numerical.
- They usually carry 6–10 marks.
- With proper practice, this topic can become a sure-shot scoring area.
🚀 Preparation Tips
- Practice previous year GATE questions regularly.
- Focus on matrix methods for solving equations.
- Understand theory (definitions & theorems) and apply them to problems.
- Make short notes with formulas, theorems, and tricks for revision.
🚀Download Notes
👉 For Linear Algebra Notes
👉 For Previous year Paper
✨ Stay consistent, and Linear Algebra will turn into your high-scoring weapon in GATE!
