If v1,...v4 are in R4 and v3 is not a linear combination of v1, v2, v3, v4 then {v1, v2, v3, v4} is linearly independent.
I'm pretty sure this statement is false but I don't know how to prove it. Can someone please help me?
Reread that statment.
Do you mean v3 is not a linear combination of v1, v2, v4..."?