# Linear Algebra Crash Course

### Requirements

- Be able to do basic Mathematical operations
- Solve simple equations like 3x +7 = 5 (x= - 2/3)

Learn the fundamentals of Linear Algebra.

**Linear Algebra fundamentals **are: Linear Systems, Matrix Algebra and Vector Spaces.

Without **these 3 pillars** it is impossible to grasp the complex subject of linear algebra. This course specializes exactly on that: Linear Systems Matrix Algebra and Vector Spaces.

This is **what you will learn** in this course:

What is a linear System

Triangular System and why they are important

What operation you are allowed to perform on any system

Solve systems with a parameter

Solve any linear System, with different number of variables and equations

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Matrices

Matrix Algebra: Sum, Difference and Multiplications

Transpose of a Matrix

Symmetric Matrices

Inverse of a Matrix and how to compute one

Determinant of Matrices and their properties

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Vectors, sum, difference and properties

Vector spaces, example and non examples

Linear combinations of Vectors

Span of Vectors

What is a base of a Vector Space, coordinates of vectors.

- Anyone interested in Linear Algebra
- People interested in a solid background for Linear Algebra
- People interested in solving very general Linear Systems
- People interested in Knowing about Vector Spaces

- Introduction03:02

- The Simplest Linear System: 1 Equation04:34

- 2 Equations Lin. System- How many solutions?09:12

- Why Linear?01:25

- General Linear System ( n Equations )04:29

- Matrix Form of Linear Systems03:42

- Triangular Systems ( Important ! )05:57

- Methods to Solve L.S.03:20

- Elimination Method Fast Overview02:03

- Permitted Change on a L.S.06:52

- Elimination Method Guide02:41

- Our First System Solved05:17

- 3 x 3 system07:44

- All Possible Cases06:47

- Systems with Parameters12:38

- How to Procede (Useful for big Systems)04:31

- Avoid Confusion in Solving L.S.04:33

- Infinite many Solutions in systems10:00

- Exercise: Lin. Syst. Solutions00:11

- Solution of the previous Exercises10:08

- Exercise 3x3 With Parameter00:12

- Solution Ex. 3x3 With Parameter07:20

- Beyond Linear Algebra...01:00

- Intro to mxn Systems (Different number of Equations and Variables)07:43

- Solution of mxn Systems02:08

- Guide to mxn Systems08:54

- Example mxn System Solved in details. 105:13

- Example 2. mxn System Solved in details.05:01

- Matrix Overview01:54

- Matrix Definition and examples05:25

- Matrix Basic Operations06:16

- Diagonal Matrices06:13

- Matrix components04:20

- Exercise Matrix 100:00

- Solution Exercise Matrix 102:44

- Exercise Matrix 200:00

- Solution Exercise Matrix 204:04

- Exercise Matrix 3: Components00:00

- Solution Exercise Matrix 3: Components03:41

- Matrix Multiplication02:33

- Matrix Multiplication-206:58

- Matrix Associative Property03:57

- Matrix Distribution Property04:24

- Linear Systems and Matrices08:47

- Exercise Matrix 300:00

- Solution Exercise Matrix 304:24

- Exercise Matrix 400:00

- Solution Exercise Matrix 405:03

- Exercise Matrix 500:00

- Solution Exercise Matrix 502:28

- Exercise Matrix 6: Lin. Syst.00:00

- Solution Exercise Matrix 6: Lin. Syst.02:17

- Transpose Matrix04:20

- Symmetric Matrix04:33

- Inverse Matrix-108:06

- Inverse Matrix-209:27

- Inverse Matrix-304:00

- Inverse Matrix-401:22

- Exercise Matrix 7 Transpose00:00

- Solution Exercise Matrix 7 Transpose02:57

- Exercise Matrix 8: Inverse00:00

- Solution Exercise Matrix 8: Inverse03:52

- Exercise Matrix 9: Inverse00:00

- Solution Exercise Matrix 9: Inverse05:52

- Solution Exercise Matrix 9 -Part 202:14

- Determinant08:37

- Determinant 3x304:23

- Determinant 4x405:30

- General computation of Determinants06:32

- Properties of Determinants06:05

- Determinants of Triangular Matrices01:47

- Vectors: Introduction05:15

- Sum of Vectors09:55

- Difference of Vectors04:45

- Vector Base06:39

- Vector Components07:11

- The Line, The Plane, The Space....06:32

- Properties of R^n06:41

- Vector Space Definition12:49

- Example of Vector Spaces05:36

- Abstract Vector Spaces: Polinomials05:10

- Non Vector Spaces08:09

- Vector Subspaces05:08

- Exercise Vector Space00:11

- Solution to Exercise04:28

- Linear Combination of Vectors08:38

- Vector Span05:12

- Span Example10:10

- More Details about Span06:54

- Linear Dependent and Independent Vector06:26

- Linear Dependent Vectors: Examples05:35

- Exercise 200:02

- Solution to Exercise 205:06

### Featured review

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