Question

Linear Algebra Question:
If dim(V)=n, then prove:
(i) Any set < n can't span V.
(ii)Any set > n can't be independent.

Answer 1

Do you mean dim(set)<n and dim(set)>n, and is\[set\subset V\]?

Answer 2

(i) Any set of size smaller than n doesn’t span the space.
(ii)A set of size n that spans the space is linearly independent, that is, if k1x1 + k2x2 + … + k(n)x(n) = 0 then k1 = k2 = … = k(n) = 0.

Need to prove this :S