Thread: linear algebra...subspaces and dimension

1) Consider two subspaces V and W of R^n ,where V is contained in W.
Why is dim(V)<= dim(W).....?
"<=" less than or equal to

2) show that if dim(V) = dim(W), then V=W

Originally Posted by Leilei

1) Consider two subspaces V and W of R^n ,where V is contained in W.
Why is dim(V)<= dim(W).....? "<=" less than or equal to
2) show that if dim(V) = dim(W), then V=W

Both of the problems require that one understands the definitions of dimension and basis, along with the relation between the two. Do you know how to those concepts. If so, the proofs are easy. Otherwise, consult you textbook.