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Linear Algebra
Lecture Schedule based on Lay – Linear Algebra and Its Applications 3rd Edition
Section  Lectures  Topic 
1.1  1  Systems of Linear Equations 
1.2  1  Row Reduction and Echelon Forms 
1.3  0.5  Vector Equations 
1.4  1  The Matrix Equation Ax = b 
1.5  1  Solution Sets of Linear Systems 
1.6  0.5  Applications of Linear Systems 
1.7  1  Linear Independence 
1.8  0.5  Introduction to Linear Transformations 
1.9  1  The Matrix of a Linear Transformation 
2.1  1  Matrix Operations 
2.2  1  The Inverse of a Matrix 
2.3  0.5  Characterizations of Invertible Matrices 
2.5  0.5  Matrix Factorizations 
4.1  1  Vector Spaces and Subspaces 
4.2  1  Null Spaces, Column Spaces and Linear Transformations 
4.3  0.5  Linearly Independent Sets; Bases 
4.5  0.5  The Dimension of a Vector Space 
4.6  0.5  Rank 
4.4  0.5  Coordinate Systems 
4.7  1.5  Change of Basis 
3.1  0.5  Introduction to Determinants 
3.2  1  Properties of Determinants 
3.3  0.5  Cramer’ s Rule ; Volume and Linear Transformations 
5.1  1  Eigenvectors and Eigenvalues 
5.2  1  The Characteristic Equation 
5.3  0.5  Diagonalization 
6.1  1  Inner Product , Length and Orthogonality 
6.2  0.5  Orthogonal Sets 
6.3  1  Orthogonal Projections 
6.4  0.5  The GramSchmidt Process 
6.5  0.5  Least  Squares Problems 
7.1  1  Diagonalization of Symmetric Matrices 
List of Topics for MATLAB laboratories:
1. Introduction to MATLAB
2. Systems of Linear Equations and FloatingPoint Errors
3. Matrix Algebra
4. Elementary Row Operations and LU Factorization
5. Linear Dependence, Column Space, Null Space, and Bases
6. Change of Basis and Coordinate Transformations
7. Eigenvalues and Determinants
8. Orthogonality and Least Squares
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