Exercise 3.3 Consider the hat matrix H X(XTX) XT, where X is an N by d+1 matrix, and XTX is invertible. (a) Show that H is symmetric. (b) Show that H H for any positive integer K (c) If I is the identity matrix of size N, show that (I-H)-H for any positive integer K (d) Show that trace(H) = d+ 1, where the trace is the sum of diagonal elements. [Hint: trace(AB) = trace(BA)/ Exercise 3.3 Consider the hat matrix H X(XTX) XT, where X is an N by d+1 matrix, and XTX is invertible. (a) Show that H is symmetric. (b) Show that H H for any positive integer K (c) If I is the identity matrix of size N, show that (I-H)-H for any positive integer K (d) Show that trace(H) = d+ 1, where the trace is the sum of diagonal elements. [Hint: trace(AB) = trace(BA)/