
Chapter 1 Exercise 8.
Prove the intersection of any collection of subspaces of V is a subspace of V .
Proof:
Let be subspaces of
.
Then . Thus,
(1)
Therefore, .
Suppose . Then
.
Since is a subspace,
. Thus
(2)
Since is a subspace,
and scalar
. Thus
(3)
By 1, 2 and 3, is a subspace of
.