2. Let id denote the identity map R^n -> R^n. Let B denote a basis B = {v1, v2, ..., vn} of R^n and let E denote the standard basis E. Compute the matrix representation of I with respect to B, E.

It is obvious to me that a surjective linear map exists if W is of lower dimension than V. I am unsure of how exactly to show this, though. For the map f: V -> W to be surjective, an f(v) (such that v is an element of V) must exist for every w (w is an element of W).

I'm unsure of what I'm attempting to do on the second problem.