Construct the normal equations for the linear polynomial least squares to fit the data x = [1 0 1], y=[3;2;1]. (a) Find the parameters of the linear regression u1, u2 using QR decomposition, and plot the data and the fit curve in a graph (paper and pencil). (b) Calculate the eigenvalues of the normal equation matrix A'*A for the above data from the characteristic polynomial. (c) Write down quadratic interpolation polynomial in Lagrange form to interpolate the three data points. (d) Assume that the normal equation matrix A'*A is generated by A with m rows and n columns, m>=n. Explain under which conditions there would be a zero eigenvalue among the eigenvalues of the matrix of the normal equations.
