please help me with all 3 questions.. Use a separate sheet of paper to write pro

ID: 2971186 • Letter: P

Question

please help me with all 3 questions..

Use a separate sheet of paper to write proofs for the following. Make sure your arguments are organized, clear, and justified. You may use any results that were proved in class. Each problem is worth 3 points. Prove that for any inner product space V: V = { v}, and { V} = V. Suppose that T: V rightarrow W is a linear transformation from one inner product space to another, such that:||v ||v= ||T( v)||w Prove that T is 1 to 1. (Hint: look at the kernel of T.) Prove that [Projw] is symmetric for every projection operator on Rn. (Hint: (AB)T = ?...)