3. Bidiagonal Least Squares with Shift. Consider the bidiagonal matrix B n-1 Pn For a shift A, you are ask to consruct the orthogonal factorization ( VAI ) - UW ( B CN) ) v where B(A) is also upper bidagonal, and the orthogonal matrices U(A) and V can be constructed using O(n) Givens rotations (or 2 x 2 House- holder matrices). [Hint: It is fairly easy to construct V such that B7 - VCT where C is lower bidiagaonal. (Show how, don't just state it, please!) Then ( JU ) - ( 5 9 ) ( 2 ) V since VVT - I. Then show how to compute the Q-R factorization of with 2n - 1 Givens rotations. You might want to work out your algo- rithms on a 3 x 3 or 4 x 4 B first.] 2