If a set of vectors is linearly dependent, does it mean any of them can be expressed in terms of the others

(that is within the rigour of a first year linear algebra course)

Yeah, that sounds right. If I have my terms correct, linear dependency means they're all in the same direction. So a formal proof would be:

All linearly dependent vectors share the same unit vector. All vectors can be expressed in terms of their unit vector times a scalar (number, not a vector). Therefore, all linearly dependent vectors can be expressed in terms of another times a scalar quantity.

EDIT: Jaf is correct about the zero (or 'null') vector, although that's often considered a trivial case. I would still recommend including that in your answer in case your teacher is a jerk.

This statement is not true. Note that any set containing the zero vector is linearly dependent. Consider the linear dependent set that consists of one non-zero vector and the zero vector. The non-zero vector may not be expressed in terms of the zero vector..