linearly independent subset in Singular

Dear friends,
I have two problems to solve with Singular:
problem 1
I have a matrix with components rational numbers
I want to select a maximal linearly independent subset from columns.

Problem 2
Note S = Q[x, y, z] and S_d = the set of homogeneous polynomials of degree d.
I have a set of vectors (f, g, h), where f, g, h are from S_d.
I want to select a maximal linearly independent vectors (S ^ 3 as a vector space over Q)

For both problems, I want a subset unchanged.

Thank you in advance