Subspaces

Question 1

Subspace

Answer 1

A subset W of a vector space V is a subspace of V if W itself is a vector space, using the same addition and scalar multiplication as for V.

Question 2

Subspace Theorem

Answer 2

Let W be a non empty subset of a vector space V. Then W is a subspace of V if and only if W satisfies both of following conditions :

u + v E W for all u,v E W i.e addition on W is closed

ku E W for all k E R and u E W i.e scalar multiplication on W is closed