# Number of linear independent subsets with cardinality 4

I have a list of vectors in the vector space Q with a dimension of 5, which I want to order in a list and use Combinations(list, 4) to get all sublists with 4 elements. I then want to check how many of those sublists are linear independent in the Vector Space with V.linear dependence(vs) == [].

I'm running into an error when running my code:

V = VectorSpace(QQ,5)

V.list = ([2, 2, 2,-3,-3],[2, 2,-3,2,-3],[2,2,-3,-3,2],[2,-3,2,2,-3],[2,-3,2,-3,2],[2,-3,-3,2,2],[-3,2,2,2,-3],[-3,2,2,-3,2],[-3,2,-3,2,2],[-3,-3,2,2,2])

C = Combinations(list, 4)

V.linear_dependence(C) == []

"ValueError: vector [[2, 2, 2, -3, -3], [2, 2, -3, 2, -3], [2, 2, -3, -3, 2], [2, -3, 2, 2, -3]] is not an element of Vector space of dimension 5 over Rational Field"

Anyone got any clues as to what im missing?

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If we define f by

def f(x, y, z):
return x * y * z

then f(2, 3, 5) returns 30 but f(2*3*5) gives:

TypeError: f() takes exactly 3 arguments (1 given)


produces:

If we define f by

def f(x, y, z):
return x * y * z


then f(2, 3, 5) returns 30 but f(2*3*5) gives:

TypeError: f() takes exactly 3 arguments (1 given)