Are these functions linearly dependent?

Question

The Wronskian of two functions is $W(t) = t^2 - 4$. Are these functions linearly dependent?

I don't think they are, since the Wronskian is only equal to zero when $t = 2$ or $t = -2$. I'm not sure though, since the Wronskian has thus far only been used in my class for functions of which we know they're solutions to a differential equation.

Question: Can you conclude that these functions are linearly independent because their Wronskian is only equal to zero at a couple of points?

Answer 1

If the wronskian of a set of function is different from zero at at least a point of the domain than the functions are linearly independent

This is a consequence of the fact that the zero element of the vector space is the null function, that is the function that has always value zero.

Answer 2

Of course we can conclude that. If they were linearly dependent, the Wronskian would be $0$ everywhere.