Linear Systems Overview
  • 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
Linear Systems Solution
  • 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...
Linear Sytems mxn ( Advanced Section )
  • 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 Intro and Algebra
  • 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 and Properties
  • 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.
Operations on Matrices
  • 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
Matrix Determinants
  • Determinant
  • Determinant 3x3
  • Determinant 4x4
  • General computation of Determinants
  • Properties of Determinants
  • Determinants of Triangular Matrices
Vectors: Basics
  • Vectors: Introduction
  • Sum of Vectors
  • Difference of Vectors
  • Vector Base
  • Vector Components
  • The Line, The Plane, The Space....
Vector Spaces
  • 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 Combinations and Span in Vector Spaces
  • Linear Combination of Vectors
  • Vector Span
  • Span Example
  • More Details about Span
  • Linear Dependent and Independent Vector