Help solving a problem in Chapter #7 of Fundamentals of Corporate Finance, Fourth Edition

NPV versus IRR. Here are the cash flows for two mutually exclusive projects: Project C0 C1 C2 C3 A -$20,000 +8,000 +8,000 +8,000 B -$20,000 0 0 +$25,000 a. At what interest rates would you prefer project A to B? Hint: Try drawing the NPV profile of each project. b. What is the IRR of each project?

Metric and polynomial

Please see attached

Isometrically isomorphic spaces

(See attached file for full problem description with symbols and equations) --- Let be the set of all sequences , such that exists. Let be the dual space of , and consist of all functions , , such that for every is finite. Show that is isometrically isomorphic to . Are and isometrically isomorphic? ---

Orthonormal set

(See attached file for full problem description with proper symbols) --- Assume that is a linearly independent set in a Hilbert space Suppose that is an orthonormal set in satisfying the following property: for each (a) Show that for each (b) Let be the orthonormal set gotten from the Gram-Schmidt procedure applied to . Show that for each , where is a complex number of modulus 1. ---

Closed graph

(See attached file for full problem description) --- Let and be Banach spaces and let . (Note: is a set of all continuous linear transformations ). Show that there is a constant such that for iff and gra is closed. ---