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Module 1: Basics of Linear Algebra
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Lecture 1A - Why Study Linear Algebra
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Lecture 1B - Linear Algebra for GATE & Interviews
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Annotated Notes - Lecture 1A-1B
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Lecture 1C - Linearly Independent and Linearly Dependent
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Annotated Notes - Lecture 1C
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Lecture 2A - Filling the Space Part 1
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Lecture 2B - Filling the Space Part 2
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Lecture 2C - Summary so far
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Lecture 2D - Multiplying a Matrix & a Vector
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Annotated Notes - Lecture 2
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Homework 1 - Linear Dependence & Independence
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Lecture 3A - Homework 1 Discussion
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Annotated Notes - Lecture 3A - Homework 1 Discussion
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Lecture 3B - Why Solve System Of Linear Equations
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Lecture 3C - Writing as Ax=b, Geometric Interpretation and Possible Solutions
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Lecture 3D - Understanding Ax=b intuitively
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Lecture 3B-D Annotated Notes
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4A. Multiplying 2 Matrices | My Walmart Interview Question
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4B. GATE 2016 Question
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4C. GATE 2014 Question
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4D. Two conceptual questions
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4E. Linear Combination of Independent vectors is unique
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4F. GATE 2017 Question
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Lecture 4 Annotated Notes
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5A. Echelon Form and Pivot Columns
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5B. Gaussian Elimination
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5C. Rank | GATE 1994 Question | Rank Nullity Theorem
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5D. Finally Solving Ax=b | Five Different Questions
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5E. More than one free variable in 𝐴𝑥=0 solution
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Lecture 5 Annotated Notes
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6A. GATE 2021 Question | Free variables in Non homogeneous
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6B. Solutions based on Rank(A) and Rank(A|b)
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6C. Few Questions related to rank(A) and Number of solutions
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6D. Linearly Independent Columns with Gaussian Elimination
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6E. Row Reduced Echelon Form
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Lecture 6 Annotated Notes
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Lecture 7A. Determinant
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Lecture 7B. Inverse of a Matrix
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Lecture 7C. Crammer's rule
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Annotated Notes Lecture 7 A-C Determinant Inverse and Cramer's Rule
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Lecture 8A. Introduction to Eigenvalues and Eigenvectors
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Lecture 8B. Characteristic Equation
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Lecture 8C. Solving for Eigenvalues and Eigenvectors
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Annotated Notes Lecture 8A-C EigenValues and EigenVectors
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Lecture 9A. Linearly Independent Eigen vectors with repeating eigenvalues
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Lecture 9B. Three Different Examples With Repeating Lambda
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Lecture 9C. Symmetric Matrices has n LI Eigen Vectors
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Lecture 9D. Two Magical Properties
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Annotated Notes Lecture 9A-D Eigen Vectors
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Lecture 10A. Rank and Eigen Values
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Lecture 10B. Examples on Rank and Eigen Values
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Lecture 10C. CAYLEY-HAMILTON THEOREM
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Lecture 10D. Eigen Values of AB and BA
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Lecture 10E. Eigen Values of Powers of A
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Annotated Notes Lecture 10A-E Rank and EigenValues
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Lecture 10F. (Three Tough/Interesting GATE PYQs)
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Annotated Notes Lecture 10F GATE PYQs Linear Algebra
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Lecture 11A. LU Decomposition
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Lecture 11B. Type Of Matrices
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Annotated Notes Lecture 11A -B
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LIVE Practice Questions on Linear Dependent Vectors
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Annotated Notes Practice Questions on Linear Dependent Vectors
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LIVE Practice Questions on Solutions of Ax = b
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Annotated Notes Practice Questions on Ax=b
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Weekly Quiz and Solution
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Module-2
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Information
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Lecture 1: Introduction to Vector Spaces, Subspaces, Basis, and Span
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Annotated Notes Lecture 1 Module 2 Definition of Vector Spaces and SubSpaces
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Lecture 2: Basis, Span, Subspaces of Matrix A (Column and Null Space)
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Annotated Notes Lecture 2 Module 2 Basis Span and Dim of Space
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Lecture 3: Subspaces of Matrix A (Column and Null Space)
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Annotated Notes Lecture 3 Module 2 Col and Null Space
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Lecture 4: Subspaces of Matrix A (Row and Left Null Space)
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Annotated Notes Lecture 4 Module 2 Row and Left Null Space
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LA for GATE DA Module-2 HomeWork-1
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LA for GATE DA Module-2 HomeWork-2
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Lecture 5: Four Fundamental Subspaces
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Annotated Notes Lecture 5 Module 2 Four Fundamental Subspaces
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Lecture 6: Change of Basis
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Annotated Notes Lecture 6 Module 2 Change of Basis
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Lecture 7: Linear Transformation
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Annotated Notes Lecture 7 Module 2 Linear Transformation
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Lecture 8: More on Linear Transformation
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Annotated Notes Lecture 8 Module 2 More on Linear Transformation
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Lecture 9: Linear Transformation w.r.t. arbitrary bases
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Annotated Notes Lecture 9 Module 2 Linear Transformation in different bases
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Lecture 10: Questions on Change of Basis and Linear Transformation
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Annotated Notes Lecture 10 Module 2 Questions on Linear Transformation and change of bases
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Weekly Quiz
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Weekly Quiz-5 Solution Discussion
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Lecture 11a: Revision Class (From Lecture 1 to 5)
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Lecture 11b: Revision Class (From Lecture 6 to 10)
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Annotated Notes Lecture 11 Module 2 Summary So far
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Lecture 12: Similar Matrices and Diagonalization
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Annotated Notes Lecture 12 Module 2 Diaognalisation
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Lecture 13: Diagonalization Questions and Gram Schmidt Orthogonalization
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Annotated Notes Lecture 13 Module 2 SVD
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Lecture 14: More on Singular Value Decomposition (SVD)
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Annotated Notes Lecture 14 Module 2 SVD
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Lecture 15: Fundamental Subspaces with Singular Value Decomposition (SVD)
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Annotated Notes Lecture 15 Module 2 SVD
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Practice Set 30 Questions on SVD
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Lecture 16: Geometry of SVD and Practice Set 30 Questions Solution
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Annotated Notes Lecture 16 Module 2 SVD
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Lecture 17: Practice Set 30 Questions Solution (Q11-Q30)
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Annotated Notes Lecture 17 Module 2 SVD More Question
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Lecture 18: Orthogonal Projections
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Annotated Notes Lecture 18 Module 2 Projection Of a Vector
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Lecture 19: Projection onto Subspace
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Annotated Notes Lecture 19 Module 2 Lecture 19 Projection onto Subspace
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Lecture 20: Projection Matrix
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Annotated Notes Lecture 20 Module 2 Projection Matrix
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Lecture 21: Weekly Quiz SVD Discussion
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Annotated Notes SVD Quiz
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Lecture 22: Partition or Block Matrices Multiplication
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Annotated Notes Lecture 22 Module 2 Partition Matrix
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Lecture 23: Block Matrices Other Operations
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Annotated Notes Lecture 23 Module 2 Partition Matrix all Operations
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Lecture 24: Positive Definite Matrices
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Linear Algebra for GATE DA Module-2 Annotated Notes
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LIVE Weekly Quiz 1 Solution
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Annotated Notes Weekly Quiz 1 Solution
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LIVE Weekly Quiz 2 Solution
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Annotated Notes Weekly Quiz 2 Solution
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Recording LIVE Weekly Quiz 3 Solution Part 1
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Annotated Notes Weekly Quiz 3 Solution Part 1
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Recording LIVE Weekly Quiz 3 Solution Part 2
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Annotated Notes Weekly Quiz 3 Solution Part-2
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