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 ,

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

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
.