- Introduction
- The Simplest Linear System: 1 Equation
- 2 Equations Lin. System- How many solutions?
- Why Linear?
- General Linear System ( n Equations )
- Matrix Form of Linear Systems

- Triangular Systems ( Important ! )
- Methods to Solve L.S.
- Elimination Method Fast Overview
- Permitted Change on a L.S.
- Elimination Method Guide
- Our First System Solved
- 3 x 3 system
- All Possible Cases
- Systems with Parameters
- How to Procede (Useful for big Systems)
- Avoid Confusion in Solving L.S.
- Infinite many Solutions in systems
- Exercise: Lin. Syst. Solutions
- Solution of the previous Exercises
- Exercise 3x3 With Parameter
- Solution Ex. 3x3 With Parameter
- Beyond Linear Algebra...

- Intro to mxn Systems (Different number of Equations and Variables)
- Solution of mxn Systems
- Guide to mxn Systems
- Example mxn System Solved in details. 1
- Example 2. mxn System Solved in details.

- Matrix Overview
- Matrix Definition and examples
- Matrix Basic Operations
- Diagonal Matrices
- Matrix components
- Exercise Matrix 1
- Solution Exercise Matrix 1
- Exercise Matrix 2
- Solution Exercise Matrix 2
- Exercise Matrix 3: Components
- Solution Exercise Matrix 3: Components

- Matrix Multiplication
- Matrix Multiplication-2
- Matrix Associative Property
- Matrix Distribution Property
- Linear Systems and Matrices
- Exercise Matrix 3
- Solution Exercise Matrix 3
- Exercise Matrix 4
- Solution Exercise Matrix 4
- Exercise Matrix 5
- Solution Exercise Matrix 5
- Exercise Matrix 6: Lin. Syst.
- Solution Exercise Matrix 6: Lin. Syst.

- Transpose Matrix
- Symmetric Matrix
- Inverse Matrix-1
- Inverse Matrix-2
- Inverse Matrix-3
- Inverse Matrix-4
- Exercise Matrix 7 Transpose
- Solution Exercise Matrix 7 Transpose
- Exercise Matrix 8: Inverse
- Solution Exercise Matrix 8: Inverse
- Exercise Matrix 9: Inverse
- Solution Exercise Matrix 9: Inverse
- Solution Exercise Matrix 9 -Part 2

- Determinant
- Determinant 3x3
- Determinant 4x4
- General computation of Determinants
- Properties of Determinants
- Determinants of Triangular Matrices

- Vectors: Introduction
- Sum of Vectors
- Difference of Vectors
- Vector Base
- Vector Components
- The Line, The Plane, The Space....

- Properties of R^n
- Vector Space Definition
- Example of Vector Spaces
- Abstract Vector Spaces: Polinomials
- Non Vector Spaces
- Vector Subspaces
- Exercise Vector Space
- Solution to Exercise

- Linear Combination of Vectors
- Vector Span
- Span Example
- More Details about Span
- Linear Dependent and Independent Vector