Question

State and prove Extension theorem for linear spaces​

Answer 1

Answer:

Theorem 7 (Basis Extension Theorem). Every linearly independent list of vectors in a finite-dimensional vector space V can be extended to a basis of V . Proof. ... Since V is finite-dimensional, there exists a list (w1,...,wn) of vectors that spans V .

Answer 2

Step-by-step explanation:

Basis Extension Theorem. Every linearly independent list of vectors in a finite-dimensional vector space V can be extended to a basis of V . Proof. ... Since V is finite-dimensional, there exists a list (w1,...,wn) of vectors that spans V