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# Is R^2 a subspace of R^3 watch

1. I'm just trying to get my head around the idea of vector spaces and subspaces, and I think I just about get the idea now. Just to clarify though, would be a subspace of the vector space ?

Thanks

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2. (Original post by Brian Moser)
I'm just trying to get my head around the idea of vector spaces and subspaces, and I think I just about get the idea now. Just to clarify though, would be a subspace of the vector space ?

Thanks

Posted from TSR Mobile
For and as usually defined isn't even a subset of .
If you view , then yes "" is a subspace of .
3. Another question, what does the notation mean?

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4. The set of all the real functions (which take real numbers to real numbers) that take 1 to 0

One such function is f(x)=x-1 (x belongs to real numbers)
5. No R^2 is not a subspace of R^3, because R^2 is not even a subset of R^3. Also even if you include the 0 vector, technically a 0 vector in R^2 = (0,0) and R^3 = (0,0,0), so in no way could you say the statement is true. However R^2 is isomorphic to the subset (x,y,0) in R^3.

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Updated: January 29, 2015
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