# Linear Algebra Crash Course

Linear Systems of any kind. Matrix Operations and Determinants .Vector Spaces in Linear Algebra
Rating: 4.6 out of 5 (421 ratings)
9,519 students
Linear Algebra Crash Course
Rating: 4.6 out of 5 (421 ratings)
9,521 students
Solve any linear system
Solve linear systems with parameters
Solve linear systems with different numbers of variables and equations
Know what is a Vector Space
Determine if some vectors are dependent or not
Linear combinations of vectors
Check if a set of vectors is a base
Know what are the coordinates of a vector in a given space

### Requirements

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

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

________________________________________________________

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.

Who this course is for:
• 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
Course content
12 sections • 106 lectures • 8h 6m total length
• Introduction
03:02
• The Simplest Linear System: 1 Equation
04:34
• 2 Equations Lin. System- How many solutions?
09:12
• Why Linear?
01:25
• General Linear System ( n Equations )
04:29
• Matrix Form of Linear Systems
03:42
• Triangular Systems ( Important ! )
05:57
• Methods to Solve L.S.
03:20
• Elimination Method Fast Overview
02:03
• Permitted Change on a L.S.
06:52
• Elimination Method Guide
02:41
• Our First System Solved
05:17
• 3 x 3 system
07:44
• All Possible Cases
06:47
• Systems with Parameters
12:38
• How to Procede (Useful for big Systems)
04:31
• Avoid Confusion in Solving L.S.
04:33
• Infinite many Solutions in systems
10:00
• Exercise: Lin. Syst. Solutions
00:11
• Solution of the previous Exercises
10:08
• Exercise 3x3 With Parameter
00:12
• Solution Ex. 3x3 With Parameter
07:20
• Beyond Linear Algebra...
01:00
• Intro to mxn Systems (Different number of Equations and Variables)
07:43
• Solution of mxn Systems
02:08
• Guide to mxn Systems
08:54
• Example mxn System Solved in details. 1
05:13
• Example 2. mxn System Solved in details.
05:01
• Matrix Overview
01:54
• Matrix Definition and examples
05:25
• Matrix Basic Operations
06:16
• Diagonal Matrices
06:13
• Matrix components
04:20
• Exercise Matrix 1
00:00
• Solution Exercise Matrix 1
02:44
• Exercise Matrix 2
00:00
• Solution Exercise Matrix 2
04:04
• Exercise Matrix 3: Components
00:00
• Solution Exercise Matrix 3: Components
03:41
• Matrix Multiplication
02:33
• Matrix Multiplication-2
06:58
• Matrix Associative Property
03:57
• Matrix Distribution Property
04:24
• Linear Systems and Matrices
08:47
• Exercise Matrix 3
00:00
• Solution Exercise Matrix 3
04:24
• Exercise Matrix 4
00:00
• Solution Exercise Matrix 4
05:03
• Exercise Matrix 5
00:00
• Solution Exercise Matrix 5
02:28
• Exercise Matrix 6: Lin. Syst.
00:00
• Solution Exercise Matrix 6: Lin. Syst.
02:17
• Transpose Matrix
04:20
• Symmetric Matrix
04:33
• Inverse Matrix-1
08:06
• Inverse Matrix-2
09:27
• Inverse Matrix-3
04:00
• Inverse Matrix-4
01:22
• Exercise Matrix 7 Transpose
00:00
• Solution Exercise Matrix 7 Transpose
02:57
• Exercise Matrix 8: Inverse
00:00
• Solution Exercise Matrix 8: Inverse
03:52
• Exercise Matrix 9: Inverse
00:00
• Solution Exercise Matrix 9: Inverse
05:52
• Solution Exercise Matrix 9 -Part 2
02:14
• Determinant
08:37
• Determinant 3x3
04:23
• Determinant 4x4
05:30
• General computation of Determinants
06:32
• Properties of Determinants
06:05
• Determinants of Triangular Matrices
01:47
• Vectors: Introduction
05:15
• Sum of Vectors
09:55
• Difference of Vectors
04:45
• Vector Base
06:39
• Vector Components
07:11
• The Line, The Plane, The Space....
06:32
• Properties of R^n
06:41
• Vector Space Definition
12:49
• Example of Vector Spaces
05:36
• Abstract Vector Spaces: Polinomials
05:10
• Non Vector Spaces
08:09
• Vector Subspaces
05:08
• Exercise Vector Space
00:11
• Solution to Exercise
04:28
• Linear Combination of Vectors
08:38
• Vector Span
05:12
• Span Example
10:10
06:54
• Linear Dependent and Independent Vector
06:26
• Linear Dependent Vectors: Examples
05:35
• Exercise 2
00:02
• Solution to Exercise 2
05:06

Instructor

Francesco Santi is a Phd Researcher and Consultant in data analysis and strategic planning .

He holds a  Phd in Applied Mathematics

With nearly 10 years of programming experience he has developed since the very start a Passion for Teaching and Consulting.

Nowadays he specializes in using his technical knowledge in business related topic such as data analysis for small business and data analysis for strategic planning