Question: Combine the results of problem II and problem I to prove that Reid's bump-reducing procedure permutes V into an upper triangular matrix QVR whenever such a permutation is possible.
Problem II: (b) when the procedure terminates, there are no column singletons in the bump.
Problem I: Consider a block-diagonal matrix
such that V11 and V33 are nonsingular upper triangular. Prove that V is a permuted triangular matrix if and only if V22 is a permuted triangular matrix.