Back To The Course Mod-01 Lec-01 Introduction to the Course Contents. Free Video Tutorials and Notes Lectures Mod-01 Lec-02 Linear Equations Free Video Tutorials and Notes Lectures Mod-01 Lec-03a Equivalent Systems of Linear Equations I: Inverses of Elementary Row-operations Free Video Tutorials and Notes Lectures Mod-01 Lec-03b Equivalent Systems of Linear Equations II: Homogeneous Equations, Examples Free Video Tutorials and Notes Lectures Mod-01 Lec-04 Row-reduced Echelon Matrices Free Video Tutorials and Notes Lectures Mod-01 Lec-05 Row-reduced Echelon Matrices and Non-homogeneous Equations Free Video Tutorials and Notes Lectures Mod-01 Lec-06 Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations Free Video Tutorials and Notes Lectures Mod-02 Lec-08 Vector spaces Free Video Tutorials and Notes Lectures Mod-02 Lec-09 Elementary Properties in Vector Spaces. Subspaces Free Video Tutorials and Notes Lectures Mod-03 Lec-11 Basis for a vector space Free Video Tutorials and Notes Lectures Mod-01 Lec-07 Invertible matrices, Homogeneous Equations Non-homogeneous Equations Free Video Tutorials and Notes Lectures Mod-02 Lec-10 Subspaces (continued), Spanning Sets, Linear Independence, Dependence Free Video Tutorials and Notes Lectures Mod-03 Lec-12 Dimension of a vector space Free Video Tutorials and Notes Lectures Mod-03 Lec-13 Dimensions of Sums of Subspaces Free Video Tutorials and Notes Lectures Mod-04 Lec-14 Linear Transformations Free Video Tutorials and Notes Lectures Mod-04 Lec-15 The Null Space and the Range Space of a Linear Transformation Free Video Tutorials and Notes Lectures Mod-04 Lec-16 The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces Free Video Tutorials and Notes Lectures Mod-04 Lec-18 Equality of the Row-rank and the Column-rank II Free Video Tutorials and Notes Lectures Mod-05 Lec19 The Matrix of a Linear Transformation Free Video Tutorials and Notes Lectures Mod-06 Lec-21 Linear Functionals. The Dual Space. Dual Basis I Free Video Tutorials and Notes Lectures Mod-04 Lec-17 Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank I Free Video Tutorials and Notes Lectures Mod-05 Lec-20 Matrix for the Composition and the Inverse. Similarity Transformation Free Video Tutorials and Notes Lectures Mod-06 Lec-22 Dual Basis II. Subspace Annihilators I Free Video Tutorials and Notes Lectures Mod-06 Lec-23 Subspace Annihilators II Free Video Tutorials and Notes Lectures Mod-06 Lec-24 The Double Dual. The Double Annihilator Free Video Tutorials and Notes Lectures Mathematics - Linear Algebra Free Video Tutorials and Notes LecturesMod-01 Lec-04 Row-reduced Echelon Matrices Free Video Tutorials and Notes LecturesLinear Algebra by Dr. K.C. Sivakumar,Department of Mathematics,IIT Madras.For more details on NPTEL visit http://nptel.ac.in