Let W be a vector space in Rn with basis B of dimension q. Dene f on W such that f maps the vectors in W to the vectors representing their...

5. Let W be a vector space in Rn with basis B of dimension q. Define f on W such that f maps the vectors in W to the vectors representing their coordinates with respect to the basis B.

(a) Prove that f defines a valid function. (b) What is the codomain of f? (c) Prove that f is onto. (d) Prove that f is 1-1.