Question
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..)
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..)