V is any vector space, where are subspace of V.

Prove U is not a subspace of the vector space V.

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- Jun 7th 2013, 05:58 AMTweetysubspace proof help
V is any vector space, where are subspace of V.

Prove U is not a subspace of the vector space V. - Jun 7th 2013, 06:31 AMswarnaRe: subspace proof help
For example, let us consider two subspaces S & T of the vector space R3 where S = {(x,y,z) : y=0 , z=0} T = {(x,y,z) : x=0, z=0}

let a=(1,0,0) belongs to S & b=(0,1,0) belongs to T. But a+b does not belong to SUT - Jun 7th 2013, 06:56 AMHallsofIvyRe: subspace proof help
You

**can't**prove this, It**isn't**true unless you have restrictions on and . For example, if the vector space is , , and then which certainly is a subspace.

What**is**true is that is a subspace if and only if one is a subspace of the other.

In order to prove this, you will have to make use of the fact, which isn't true unless one is NOT a subspace of the other, that there exist a vector u in that is not in and that there exist a vector v in that is not in .