Compute the eigenvalues and eigenvectors of the symmetric tridiagonal matrix with diagonal entries all zero and off diagonals k/√ 4k2 − 1 (cf. the Gauss–Legendre quadrature XXXXXXXXXX)). Show that X+y...

Compute the eigenvalues and eigenvectors of the symmetric tridiagonal matrix with diagonal entries all zero and off diagonals k/√ 4k2 − 1 (cf. the Gauss–Legendre quadrature (10.2.12)).

Show that X+y has the shortest length of all solutions to the normal equations XTXb = XTy.