Consider the knots xi = i−1 n−1 , i = 1,... ,n, and design points uj = j N , j = 1,... ,N. a) For n = 10 and N = 50 and degree p = 3, construct the design matrices XT using the truncated power basis...

Consider the knots xi = i−1 n−1 , i = 1,... ,n, and design points uj = j N , j = 1,... ,N. a) For n = 10 and N = 50 and degree p = 3, construct the design matrices XT using the truncated power basis and XB using B-splines. b) Find the linear transformation C such that XB = XT C. c) Compute the condition numbers for XT and XB. d) Repeat with varying values of n, N, and p.