it is not a subspace because there is no additive identity in U

it is not a subspace because there is no multiplicative identity in

not a subspace of

1 dimensional subspace of

2 dimensional

subspace of

3 dimensional

subspace of

-1

0

1

2

Every subspace of a vector space is itself a vector space

The union of any two subspaces of a vector space is a subspace of V

The intersection of any two subspaces of a vector space is a subspace of V

Every Vector space is a subspace of itself