Linear Independence: Combining Basis A & B to Create C

[lubuntu]

Homework Statement

Suppose B and A are a basis in vector space V, dimension N, now if I can any linear independent columns of basis B and A can I combine them to make a new basis C provided that all the all, even the unused vectors of bases A & B linear combinations of C.

Homework Equations

The Attempt at a Solution

I guess the key thing to do here would be to look at the null space of C and see how it compares to A, if this is a problem in R^n then if the null spaces where the same then so would be the basis. So I guess I am just looking for a general method of figuring out if the span of two column spaces are the same, is the question posed true or false?

 

[Mark44]

Homework Statement

Suppose B and A are a basis in vector space V, dimension N, now if I can any linear independent columns of basis B and A can I combine them to make a new basis C provided that all the all, even the unused vectors of bases A & B linear combinations of C.

Huh? There seem to be some words missing. Please provide the exact problem description.

The Attempt at a Solution

I guess the key thing to do here would be to look at the null space of C and see how it compares to A, if this is a problem in R^n then if the null spaces where the same then so would be the basis. So I guess I am just looking for a general method of figuring out if the span of two column spaces are the same, is the question posed true or false?