Right-ho. Then the way I would go about it is this: let the columns of
be denoted
They are column vectors in
Let
be an arbitrary vector in
We want to know if there is a set of scalars,
such that
right? Now, this equation that I've just written down can be translated into a system of equations for the unknown constants
Your goal is to determine the rank of the coefficient matrix for that system. If the rank is 4, then you've got yourself a spanning set with those
's. Otherwise, if the rank is less than 4, you don't. Make sense? Where would you go next?