Calculating the kernel of a matrix - An example

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This is my video series about Linear Algebra. We talk about matrices, linear maps, eigenvalues, eigenvectors, basis, linear span, linear independent sets, and a lot more. I hope that it will help everyone who wants to learn about it.

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00:00 Introduction
00:08 Example with a 3x4 matrix
00:32 Definition of the kernel
01:53 Row operations don't change the kernel
03:10 Creating zeros in second column
03:54 Row echelon form
04:45 Stating equation with variables
05:36 Backwards substitution
06:50 Solution set
07:45 Rewriting solution set as a span
08:30 Basis of the kernel

#LinearAlgebra
#Vectors
#Matrices
#MachineLearning
#Eigenvalues
#Calculus
#Mathematics

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

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