Exercise 5.2 a. Calculate WTW. What do you get? Why should we expect this result? b. Enter the following vectors into MATLAB: a = 0 b = Compute the norm of b and the norm of Wb. What do you notice? Also compute the dot products (a, b) and (Wa, Wb). One of the fundamental properties of orthogonal matrices is that they preserve norms of vectors and the standard inner product. (You can define orthogonal matrices as the ones with this property, in fact.) c. The columns of W are linearly independent because the vectors are orthogonal, so W should clearly be invertible. Use inv(W) to compute the inverse of W, and then compare it to WT. What do you observe?