How to Prove a Set is a Subspace of a Vector Space
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How to Prove a Set is a Subspace of a Vector Space
Comments
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This topic is soooo confusing, is like adopting your brain to a new type of math that sometimes has no sense
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prove x= 0 is a vector space?
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this is a great video, but I don't not get the first prove, V not equal when you also wrote 0+0=0. doesnt that mean V is 0??!?! I'm confused thsnks
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with this proof of the addition lets assume i wanna proof that x2+y2 = ( x1+y1)+(x3+y3) is a subset, so my question is, how can it be that x2+y2 is a subset of x3+y3 and simultaneously x3+y3 is a subset of x2+y2 ?
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Clicked on the video, heard it wasn't Khan, went to find a new video.
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Awesome video. Thanks. Just one kindly suggestion that you can do that may help someone really slow like me, maybe you could elaborate just a bit more on the proof or thought process going into the proofing that vector zero exist.
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What exactly does it mean for a vector to be non-empty...
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Linear Algebra seems so uninteresting compared to Calc 3...
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first note that the zero sequence, a_n = 0 for all n is bounded since |a_n| = 0 <= M, for any M > 0
Then just take two bounded sequences say a_n and b_n with bounds M and L, and look at the sum a_n + b_n,
|a_n + b_n| <= |a_n| + |b_n| < M + L, so the sum is bounded, then just look at the scalar product, c*a_n and note |c*a_n| = |c|*|a_n| < |c|*M
that's the idea, just write it a bit more formally -
How can I prove, using this, that the subset of all bounded sequences (of real numbers) is a subspace of the set of all sequences of real numbers? Thanks!
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Damn, thanks! As they say; 'You da man'
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i cant uderstad any ting he says
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Thank you so much. you made it so easy to understand. you're indeed a Math Sorcerer
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Is "The zero vector is in W" not the first condition? I know that if 0 is in W then W is not empty obviously but if W is non-empty then there is no guarantee it has the zero vector. My question again is: Is it mandatory for the 0 vector to be in W? My course has taught me all subspaces of V must have the 0 vector, else it is not a subspace. Or maybe I understood wrong.
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Perfect! I now completely understand, amazing!
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thanks! this totally helped; I'm just still kinda wondering what it'd be like if the set isn't a subset of vector space
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your not explaining why fail
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thanks :)
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