MTH-522-HomeWork1.pdf - MTH... * MTH 522 : 5 Homework 2 This homework serves as a practice to the lecture on the Hat matrix Grading: 70% problem 1 and 30%. Please describe your results and include R code, and put everything a SINGLE document to submit. 1. In the toy data example (price Vs age of used car). a) What is the Hat matrix? b) Verify that the Hat matrix is symmetric and idempotent. c) Verify that all diagonal entries are in the range of [0, 1]. d) What is the trace of the Hat matrix? 2. Verify the following property of matrix trace trace(AB)=trace(BA) by running the following R code three times: A