
 a) Verify with numeric applications,
    some vector space axioms on (rows, 
    columns) vectors and  on polynomial.
 
 b) The coefficients, integers or fractions, are randomly
    selected by the computer.

 c) The size of the vectors, are randomly selected by the 
    computer, but you can select the size if you want.

 
    Try the examples in this order.


        vaF.c,     vaI.c  :        u + v = v + u          
        vbF.c,     vbI.c  :  (u + v) + w = u + (v + w)
        vcF.c,     vcI.c  :        0 + u = u + 0    = u        
        vdF.c,     vdI.c  :     u + (-u) = (-u) + u = 0          
        veF.c,     veI.c  :     k( u+ v) = ku + kv
        vfF.c,     vfI.c  :    (k + l) u = ku + lu
        vgF.c,     vgI.c  :       k (lu) = (kl) u
        

                   paI.c  :        p + q = p + q          
                   pbI.c  :  (p + q) + r = p + (q + r)
                   pcI.c  :        0 + p = p + 0    = p        
                   pdI.c  :     p + (-p) = (-p) + p = 0          
                   peI.c  :     k( p+ q) = kp + kq
                   pfI.c  :    (k + l) p = kp + lp
                   pgI.c  :       k (lp) = (kl) p

                                           
