Let Q be an n Atilde n orthogonal matrix Show that (a) Q 1 (b) cond2(Q) 1 (c) For any b Rn, the relative error in the solution to Qx b is equal to the relative residual that is,1 ell rll2 2

Question: Let Q be an n Ã n orthogonal matrix. Show that (a) ||Q|| = 1 (b) cond2(Q) = 1 (c) For any b Rn, the

Let Q be an n Ã— n orthogonal matrix. Show that
(a) ||Q|| = 1
(b) cond2(Q) = 1
(c) For any b ˆˆ Rn, the relative error in the solution to Qx = b is equal to the relative residual; that is,1

ell rll2 2

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