Week  Topics  Study Materials  Materials 
1 
Introduction. Linear systems and matrices.


Chapter 1.1

2 
Elementary Row Operartions. Gaussian Elimination Method.


Chapter 1.2

3 
Matrix Algebra


Chapter 1.3

4 
Inverse of a Square Matrix. Techniques for Finding Matrix Inverse.


Chapter 1.4, 1.5

5 
Determinants. Cramer's Rule.


Chapter 2.1, 2.2, 2.3

6 
LU and Cholesky decompositions


Chapter 9.1

7 
Vector Spaces and Subspaces


Chapter 3.1, 4.1, 4.2

8 
Spanning Sets. Linear Independence.


Chapter 4.3 and 4.4

9 
Basis and Dimension


Chapter 4.5, 4.6, 4.7

10 
Row, Column and Null Spaces. RankNullity Theorem


Chapter 4.8, 4.9

11 
Eigenvalues and Eigenvectors of Matrices


Chapter 5.1, 5.2

12 
Diagonalization of Matrices


Chapter 5.2, 5.3

13 
Applications. Difference and Differential Equations


Chapter 5.4

14 
Jordan Normal Form


