I want to find the most compact representation of a vector as a linear combination of a set of vectors B. B has more elements (on purpose) that is needs to have to describe the subspace.

For example

    1 0 0 0
    0 1 0 0
    0 0 1 0
    0 0 0 1
    0 1 1 0

Given 

    0 2 2 1

I want to obtain:
    
    0 0 0 1 2

and not

    0 2 2 1 0