Transformation matrix from R8 to R4

Hi everybody, I have a problem regarding a matrix base transformation. My matrix (let's call it B) is a (4x8) one. It, therefore, multyplies a (8x1) vector (u) to obtain four equations. I need to find from that, a reduced matrix of order (4x4) (call it O) and a a vector v (4x1); such that v is a linear combination of elements of u. Also, O*v should give the same four equations of B*u (once substituted elements of u in v). Is there a command, or a funtion to obtain this, simplifing the computation? It is quite urgent. So if anyone has a suggestion, please write it here.

Thanks a lot.