Thm 1.11: For subspace W⊆V: (a) W is finite-dimensional & dim(W) ≤ dim(V). (b) dim(W) = dim(V)⇒V=W.

Theorem 1.11: Let W be a subspace of a finite-dimensional vector space V.
Then
(a) W is finite-dimensional and dim(W)≤ dim(V).
(b) dim(W)= dim(V) ⇒V=W.

Corollary: If W is a subspace of a finite-dimensional vector space V,
then any basis for W can be extended to a basis for V.

Видео Thm 1.11: For subspace W⊆V: (a) W is finite-dimensional & dim(W) ≤ dim(V). (b) dim(W) = dim(V)⇒V=W. канала MathPi