Thread: vector space t/f question

T/F prove...

a)The intersection of any two subsets of V is a subspace of V
b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.

can sum1 provide a proof for these?

Originally Posted by ruprotein

T/F prove...

a)The intersection of any two subsets of V is a subspace of V

The intersection of two subspaces is again a subspace, correct.

b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.

can sum1 provide a proof for these?

Not true, consider a vector space with dimension 1, then any subspace must have dimension 1 also, because it cannot be larger and it cannot be less because it is 1.

Originally Posted by ruprotein

a)The intersection of any two subsets of V is a subspace of V.

Did you mean subspaces but wrote subsets.
It is false if it is subsets.

b) If V is a vector space other than the zero vector space, then V contains a subpace W such that W doesnt equal V.

True! If V is not {0}, then take W={0}.