How to Find the Basis of a Subspace

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In this video we try to find the basis of a subspace as well as prove the set is a subspace of R3! Part of showing vector addition is closed under S was cut off, all it says is 2*y2 + 3*y3. We then make the substitution that it equals y1 on the following line.
  1. Drew Werbowski
  2. math
  3. linear algebra
  4. tutor
  5. subspace
  6. basis
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Комментарии
Автор

Thank you man, i would never have thought this (finding a basis for a linear subspace) was that easy to do.

dansheldon
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grateful for the existence of this video, thanks

ammaryildirim
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Good video, but can I ask something. Since the definition of a bases states that not only must the list be linearly independent but must also span the entire vector space. How do we prove that or is it not necessary for this proof?

The-Collector-gq
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Does it matter which variables I choose as my free ones? I’m having trouble finding anything regarding this as I have chosen different free variables and have a different answer

Johnny-vxeh
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How can the dimension be less than 3 if they are basis

namansingh
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By the way, could you explain to me one thing please. If we want to define a linear subspace by saying it is closed under addition and multiplying by a constant, do we really need to say there also has to be an [0, 0, ...0] (for R^n) element in our subspace? If it is proven that any vector of our space multiplied by some constant is also in the space, can't we just say that as the constant is basically every real number it is also zero as well, so [0, 0, ...0] vector is just V * c, where c = 0?

dansheldon