The most direct way is to use the

**definition** of "linear indepdence" and "linear dependence":

If there exist numbers,

,

, ...,

,

**not all 0**, such that

, where that "0" is the 0 vector, then the vectors

,

, ...,

are

**dependent**, if not, then they are

**independent**.

So you start by setting up the linear combination

which, here, is

where that "0" is the 0

**function**, f(x)= 0 for all x.

Now you can "combine like terms" and use the fact that if a polynomial is 0 for all x then all coefficients must be 0 to get three equations to solve for a, b, and c. Since all three equations will be "= 0", the have the obvious solution a= b= c= 0. If that is

**only** solution, then the vectors are independent. It that solution is not

**unique**, if there exist other, non-zero, solutions, then they are dependent.

(You don't have to actually find a, b, and c. You can use the fact, if you aready know it, that a system of equations has a unique solution if and only if the determinant of the coefficient matrix is non-zero.)