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