B=random_matrix(QQ,5,5)
B
print 'Macierz B \n'
wyzn=B.determinant()
wyzn
print 'Wyznacznik B \n'
i=0
for i in range(5):
    vi=vector(B[i,:])
    for j in range(i):
        vj=vector(B[j,:])
        q=(vi.dot_product(vj))/(vj.dot_product(vj))
        vi=vi-(q*vj)
    B[i,:]=vi

B
print 'Zmieniona macierz B \n'