If you want to know if two parameters are linearly dependent, there are two ways. One would be to put them in a linear combination and if at least one coefficient cannot be zero (i.e you can represent one parameter in terms of another), then they are linearly dependent. If these parameters are all dependent on a common variable, you can use Abel's Identity and take the Wronskian of them, if it is equal to zero over the entire interval of the common variable then the two parameters are linearly dependent.

There are probably other ways (in fact, I know there are...), but these two are pretty easy.