# Span linear

posted by
**Anatoly Z** on
.

hello everyone!i'm breaking my head and desperate how to do it...

If i have a vector in linear space V:r v1,v2.....vk,a,b

having A={v1,v2.....vk,a} B={v1,v2....vk,b} C={v1,v2...vk}

and its known that V=sp(A) and b∉sp(C)........

needed to prove

1) a ∈ sp(B)

2) V=span(B)

3) if C not linear depended-->A is basis for V??

thank you very much..(generaly i has a clue but has no idea how its correctly writing the mathematical proof..)