Let H be the set of all points in the xy-plane having at least one nonzero coord

Question

Let H be the set of all points in the xy-plane having at least one nonzero coordinate: H = {[x y]: x, y not both zero}. Determine whether H is a vector space. If it is not a vector space, determine which of the following properties it fails to satisfy: A: Contains zero vector B: Closed under vector addition C: Closed under multiplication by scalars H is not a vector space;fails to satisfy all three properties H is not a vector space;does not contain zero vector H is not a vector space;does not contain zero vector and not closed under multiplication by scalars H is not a vector space;not closed under vector addition

Explanation / Answer

H is not a vector space; does not contain zero vector and not closed under multiplication by scalar.

As (x,y) both can't be zero so the vector can't be zero.

Not closed under multiplication by scalar. As (x,y) both can't be a multiple of a number all the time

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