Exercise 2. 1) Suppose T : V → V is an operator on the inner product space V, with dim V = 4. Suppose dim(null T) = 1, what is the dimension of (range T)+? 2) Consider R? with its Euclidean inner...

Extracted text: Exercise 2. 1) Suppose T : V → V is an operator on the inner product space V, with dim V = 4. Suppose dim(null T) = 1, what is the dimension of (range T)+? 2) Consider R? with its Euclidean inner product. Suppose u = and v = If U = Span(v) and Pu(u) = v, what does b have to be equal to? Answer: 2 1 3) Consider R' with its Euclidean inner product. Let L be the line spanned by the vector (2 in R³. If ū = which one of the following vectors is the orthogonal projection PLv of ī on L? (10) d) ( 20 30 a) (2 b) (4 c) 3 4) Suppose u, v E V, where V is an inner product space, and ||u|| = || || = 1 and (u, v) = 1. Find u – v. 5) Suppose U and W are finite-dimensional subspaces of the inner product space V, with WCU. Find Pw Py.