Finding a Basis for the Nullspace or Column space of a matrix A

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Description: Two important subspaces associated to any matrix A are Null(A) and Col(A). We can look at the RREF form to quickly determine a basis for these subspaces

Learning Objectives:
1) Find a basis for Null(A) given a matrix A
2) Find a basis for Col(A) given a matrix A

This video is part of a Linear Algebra course taught at the University of Cincinnati.

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Комментарии
Автор

Watching this in preperation for my Linear Algebra final and you just gave me the biggest Aha moment

reilandeubank
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Fantastic series love from Pakistan. I have a question that in the original matrix we have the 4 column vectors in 3D out of which two are linearly dependent which means that the other two are forming a plane which is the span of the original vector. But how can s and t be in 4D for the null vector. In 3D vector space how can we write the condition for the null vectors to be in the 4D.

syedabdullah
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After watching this I feel like Danny Devito in Always Sunny

mental
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There is an error: x2 is the free variable so you set it to s, then what you need is x3 = -3t

Thewerwolf