Show solutions

5. (9 points) In this problem we look at linear transformations T: R2 - R2 such that To T(a) = T(I) for all a e R2. (a) Explain in a few sentences why an orthogonal projection onto L in R2, where L is a line through the origin, satisfies To T(x) = T(x) for all a E R2. (b) Consider now the linear transformation T(T) = Ax for all T E R2, with the matrix A = Note this T satisfies T o T(x) = T(x) for all a E R2 (you do not need to show this but can use it if you want). Explain in a few sentences why this T is not an orthogonal projection onto a line through the origin in R2. If you find yourself writing more than a few sentences, you might be on the wrong track and should find a more concise answer. We will not grade an answer which is a page long or more