Generate random linearly independent polynomials on MATLAB

I would like to create a set of K random linearly independent polynomials of M-th order on MATLAB. I came across this question on StackOverflow but I am not sure of its linear independence; and I am not looking to make it binary as mentioned in the referred question.

I tried using:

P = rand(K,M);

Will this give me K random linearly independent polynomials of M-th order?