If a vector space has a basis consisting of 5 vectors then for ,
is linearly dependent. is linearly independent.
If a vector space has a basis consisting of 5 vectors then for ,
spans . does not span .

Determine the dimensions of and .




Determine the dimensions of and .




Determine the dimensions of and .




Determine the dimensions of and .




True/False: A plane in is a two dimensional subspace of
True False
A plane in that doesn’t intersect the origin is not a subspace, so couldn’t be a subspace of dimension 2.

True/False: If and is a linearly independent set with vectors, then is a basis fo .
True False