See Wikipedia for an example.
It's always good to start with the definitions. A set of vectors, [tex]\{v_1, v_2, v_3, \cdot\cdot\cdot, v_n\}[/itex] are "independent" if and only if the only way we can have
is to have .
In this example, you would have
.
That is, you have the three equations:
If the only solution to those three equations is then the vectors are independent. If there are other solutions (a system of n homogeneous linear equations in n unknowns has a single unique solution, or has an infinite number of solutions) the vectors are dependent.