of a vector
space 
have to be a vector subspace?
(1) What two properties must a non-empty subset
of a vector
space
have to be a vector subspace?
(2) In 
what
geometrical objects are vector spaces of dimension 2?
What about of dimension 1?
(3) With each 
the span
is a vector subspace of 
.
Verify this statement using the subspace theorem.
If 
, what is the maximum dimension
of the subspace? (c.f. Span q.4)
(4) For 
a
matrix, the solution
space of 
is a
subspace of 
.
True or false.
(5) If the rank of 
is
, what is the
dimension of the subspace of (4)?
(6) The rank is equal to the dimension of what subspaces related to 
?
(See Matrix equations q.6)