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