STUDY MATERIAL · GATE DA
GATE Linear Algebra: questions and notes
Linear Algebra questions from 3 GATE papers (2024–2026) with the official answers, each solved step by step, plus notes for each topic, a formula sheet and practice questions.
- previous-year questions
- 19previous-year questions
- solved step by step
- 19solved step by step
- GATE papers, 2024–2026
- 3GATE papers, 2024–2026
- topics with notes
- 5topics with notes
TOPICS
Five topics, in the order they are taught
Taken from the official GATE 2027 syllabus. Each topic has notes, the formulas you need, its previous-year questions with the official answers and step-by-step solutions, and practice questions.
Vector spaces, subspaces, and linear dependence and independence
A vector space is a set closed under addition and scalar multiplication, and a subspace is a subset that is itself a vector space.
3 previous-year questions · 4 marks · 5 practice questions
Projection, orthogonal, idempotent and partitioned matrices, and quadratic forms
Orthogonal, idempotent and projection matrices, partitioned (block) matrices, and quadratic forms with their definiteness tests.
7 previous-year questions · 13 marks · 6 practice questions
Systems of linear equations, Gaussian elimination, rank and nullity
A system of linear equations Ax=b is solved by row-reducing its augmented matrix.
2 previous-year questions · 3 marks · 5 practice questions
Eigenvalues, eigenvectors and determinants
The determinant of a square matrix is one number that says whether the matrix is invertible and how it scales volume.
6 previous-year questions · 8 marks · 5 practice questions
Projections, LU decomposition and singular value decomposition
Projections, LU decomposition and the SVD each break a matrix problem into easy pieces.
1 previous-year question · 2 marks · 5 practice questions
QUESTIONS BY TOPIC AND YEAR
19 questions, by topic and year
How many questions each topic had in the DA papers of each year. This shows what was asked, not what will be asked. We placed each question under a topic ourselves; the exam paper does not label topics. Every question links back to its paper.
| Topic | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|
| Vector spaces | 1 | 1 | 1 | 3 |
| Special matrices | 1 | 3 | 3 | 7 |
| Linear systems | 1 | 1 | · | 2 |
| Eigenvalues | 2 | 3 | 1 | 6 |
| LU & SVD | 1 | · | · | 1 |
All three GATE DA papers are included: 2024 (IISc Bengaluru), 2025 (IIT Roorkee) and 2026 (IIT Guwahati), each with its final answer key.
Linear Algebra formulas by topic
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THE OFFICIAL SYLLABUS
What each paper lists under Linear Algebra
From the GATE 2027 syllabus PDF: all of DA Section 2, “Linear Algebra”. Principal component analysis, which rests on eigenvectors, is on the Machine Learning page.
GATE DA
Vector space, subspaces, linear dependence and independence of vectors, matrices, projection matrix, orthogonal matrix, idempotent matrix, partition matrix and their properties, quadratic forms, systems of linear equations and solutions; Gaussian elimination, eigenvalues and eigenvectors, determinant, rank, nullity, projections, LU decomposition, singular value decomposition.
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