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what is the diffrence between a vector subset and vector subspace
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a subset just doesnt match the requirements of a subspace
all subspaces are subsets; but not all subsets are subspaces
dont both have to satisy the ten axioms
no
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V and W are both subsets of R^2 but only V is a subspace of R^2
no linear combination of W will produce the 0 vector so its not a subspace ...
ahh i get it
a subspace is itself a vector space, so must satisfy all the vector space axioms
if you have a subset, it will inherit many of the properties you need, but not all. for example, as amistre pointed out, it may not contain the zero vector
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