Hi, I sort of understand how to prune just number vectors, but these polynomial type questions i am finding a bit tricky, here is one of the questions.

Let P_{3}(R) denote the vector space of real polynomial functions of degree less than or equal to three. Consider the subset X = \{f1, f2, f3, f4\} \subset P_{3}(R) with
f_{1}(x) = 3x^3 + 2x^2 - x +7,
f_{2}(x) = 7x^3 + 5x^2 + 4x + 3,
f_{3}(x) = x^3 + x^2 + 6x - 11,
and f_{4}(x) = 11x^3 + 8x^2 + x + 2.

Prune X to produce a linearly independent subset Y such that Span(Y) = Span(X).