W is not a subspace of th evector space. Verify by giving a specific example that violates the test for a vector subspace. W is the set of all vectors in R3 whose third component is -1.

Question

W is not a subspace of th evector space.  Verify by giving a specific example that violates the test for a vector subspace.  W is the set of all vectors in R3 whose third component is -1.

kinggeorge · Answer

Well, what's the test for being a subspace?

turingtest · Answer

I mentioned the tests for a subspace on a previous post
checking for closure under scalar multiplication or addition will quickly show that this is not a subspace.

turingtest · Answer

@kate003 you there?

anonymous · Answer

I'm back. Sorry had to take care of something..  so I got the answer: (0,0,-2) so it' not closed under addition neither multiplication. Thank you for the explaination :)