A spanning set that is not linearly independent

Question

What is an example of a spanning set that is not a linearly independent set? I'm having trouble trying to figure it out.

Answer 1

You can just take any basis, and add one redundant vector to it, such as the zero vector, or a linear multiple of a vector already in your set, or a linear combination of vectors already in your set. In any of these cases (the first being a special case of the second, which is a special case of the third), if you start with a spanning set, you end up with a spanning set with a dependence relation, i.e., one that is not linearly independent.

Answer 2

Taking the whole space always works because it has $0$.