compute the reduced qr

Problem 3. Let A= E E where e is a small positive number (e.g., 10-7) so that e can be ignored numerically. (a) Compute the reduced QR factorization A = QR using the classical Gram-Schmidt algorithm by hand. (b) Compute the reduced QR factorization A = QR using the modified Gram-Schmidt algorithm by hand. (c) Compute the full QR factorization A = QR using the Householder triangularization by hand. (d) Check the quality of these results by computing the Frobenius norm of IIQ Q -IIIF for the results obtained by the CGS and MGS algorithms and IIQ Q-IllF for the result obtained by the Householder triangularization