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Linear Algebra Crash Course

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Linear Systems of any kind. Matrix Operations and Determinants .Vector Spaces in Linear Algebra

What does this course teach you?

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 Linear Dependent Vectors: Examples Exercise 2 Solution to Exercise 2
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