Work out the following problem by hand. Consider the overdetermined system [1/1][x]= [9/5] whose coefficient matrix obviously has full rank.
a. Before you do anything else, guess the least-squares solution of the system.
b. Calculate a full QR decomposition of the coefficient matrix, where Q is 2 × 2 and R is 2 × 1. Use the QR decomposition to calculate the least-squares solution. Deduce the norm of the residual without calculating the residual directly.