Linear independence, yet Wronskian is zero?

Question

Why is the following set linearly independent for all x on ($-\infty$, $\infty$)?

$$\{1+x, 1-x, 1-3x\}$$

The Wronskian is $0$, but Wolfram Alpha says it is still linear independent? Why is this?

Thanks!

http://www.wolframalpha.com/input/?i=Is+%7B1-x%2C+1%2Bx%2C+1-3x%7D+linearly+independent%3F

Answer 1

Hint:

Since the Wronskian is zero, no conclusion can be drawn about linear independence.

For linear independence, we want to go back to the basic definitions.

Can you proceed?

Answer 2

You have three polynomials of degree $1$ hence they cannot be linear independent.