Question

Linear Alg : vector spaces and subspaces
What do they mean -subset, " H is a subset of the vector space V " .

Answer 1

every vector in H is also in V but not necessarily the other way around

Answer 2

if A = {1,2,3,4,5,6}
one subset is {1,2,3,4} another is {1,2,3,4,5} another is {1}

Answer 3

In Fact if H is a subspace of the Vector space V....then H is a subset of the vector space V
to not get confused ! A Subspace is a Subset wich we have

\[\forall scalar \lambda \forall x \in H \forall y \in H \]
we have \[x + \lambda y \in H \]