c1*p+c2*q+c3*r+c4*s=0

notice that we can write this in the following form:

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is a 5x4 matrix who's columns are the vectors p,q,r and s.

so we've basically got a system of homogeneous equations of the following form:

so showing that the vectors are linearly dependent is equivalent to showing that A does not have a full rank, which can be tested using the fucntion rank: rank(A) < 4