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The complete, exam-focused guide to Linear Algebra for GATE DA — from vector spaces and eigenvalues to SVD and LU decomposition. Full syllabus, topic weightage, PYQ patterns, and the best course to score every mark.
Linear Algebra is one of the highest-weightage topics in GATE DA, typically worth 8–12 marks. The full syllabus covers vector spaces, subspaces, linear independence, matrices (projection, orthogonal, idempotent, partition), quadratic forms, systems of linear equations, Gaussian elimination, eigenvalues & eigenvectors, determinant, rank, nullity, projections, LU decomposition, and singular value decomposition (SVD). The highest-yield areas are eigenvalues/eigenvectors, rank & nullity, systems of equations, and SVD. Piyush Wairale's GATE DA Linear Algebra course covers all of this with GATE-pattern practice and a test series.
Linear Algebra sits at the core of GATE Data Science & AI. It appears directly in the Engineering Mathematics section, and its concepts underpin Machine Learning, Probability & Statistics, and data analysis. Mastering it delivers a double benefit: you score direct marks and build the foundation for higher-weightage ML topics like PCA, regression, and dimensionality reduction.
Topics such as eigen-decomposition and singular value decomposition (SVD) are not just Linear Algebra questions — they are the mathematical engine behind Principal Component Analysis and matrix factorization used throughout Data Science. This makes Linear Algebra the single highest-return chapter to master for GATE DA 2027.
Every topic below is officially part of the GATE Data Science & AI Linear Algebra syllabus. Our course covers each one with theory, solved examples, and GATE-pattern questions.
Based on GATE DA and GATE CS/EC previous-year patterns, here is how the topics rank in exam importance. Prioritize the high-importance areas first.
| Topic | Exam Importance | Typical Question Style |
|---|---|---|
| Eigenvalues & Eigenvectors | Very High | Numerical (NAT), properties, diagonalization |
| Rank & Nullity | Very High | Rank-nullity, solvability of systems |
| Systems of Linear Equations | Very High | Consistency, number of solutions |
| Singular Value Decomposition (SVD) | High | Conceptual, singular values, ML link |
| Determinant | High | Numerical, property-based |
| Special Matrices (Projection/Orthogonal/Idempotent) | Medium-High | Property identification, eigenvalues |
| LU Decomposition | Medium | Factorization steps, computation |
| Quadratic Forms | Medium | Definiteness, matrix representation |
| Vector Spaces & Independence | Medium | Basis, dimension, independence tests |
Follow this sequence to build concepts logically and avoid gaps:
A dedicated, syllabus-mapped course covering every Linear Algebra topic for GATE Data Science & AI — with concept lectures, solved GATE-pattern problems, and topic-wise tests. Built by an IIT Madras M.Tech who has taught the IIT Madras BS Degree Programme.
Former instructor, IIT Madras BS Degree Programme • Microsoft Learn, AWS Academy & NPTEL Educator • 20,000+ students & 44,000+ YouTube subscribers.
The GATE DA Linear Algebra syllabus covers 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, and singular value decomposition (SVD).
Linear Algebra is one of the highest-weightage topics in GATE DA, typically carrying 8–12 marks. It is also foundational for Machine Learning, Probability, and Data Science topics, making it the single most valuable area to master for GATE DA 2027.
The most frequently tested topics are eigenvalues and eigenvectors, rank and nullity, systems of linear equations, determinants, singular value decomposition (SVD), and special matrices (projection, orthogonal, idempotent). SVD and eigen-decomposition are especially important because they connect directly to Machine Learning topics like PCA.
The GATE DA Linear Algebra course by Piyush Wairale (M.Tech, IIT Madras) is designed specifically for the GATE Data Science & AI syllabus. It covers all topics from vector spaces to SVD with GATE-pattern PYQs, solved examples, and a full test series at piyushwairale.com.
Start with vector spaces, subspaces, and linear independence, then matrices and their properties. Next master systems of linear equations and Gaussian elimination, followed by determinant, rank, and nullity. Finally focus on the high-yield advanced topics: eigenvalues and eigenvectors, LU decomposition, and singular value decomposition. Practice GATE PYQs after each topic.
Yes. Singular value decomposition (SVD) is explicitly listed in the GATE DA Linear Algebra syllabus, along with LU decomposition, eigenvalues and eigenvectors, and projections. SVD is high-importance because it links Linear Algebra to Machine Learning and dimensionality reduction.
Get the full syllabus, concept lectures, GATE-pattern practice, and test series — built for GATE Data Science & AI aspirants.