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Cinitiator
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Homework Statement
Is a set of n-tuples which must respect the conditions of closure under addition and closure under scalar multiplication a vector space or a vector subspace?
That is, in a 3-dimensional space, are planes which pass by the origin considered to be subspaces of the 3-dimensinal space in question? Or are they considered to be vector spaces?
The place where I was reading about it said that subspace of R n and Euclidean vector space are the same thing, but I'm not sure whether it's true or not. I probably misunderstood something.
Homework Equations
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The Attempt at a Solution
Posting here, as well as Googling.