Homepage › Solution manuals › Gilbert Strang › Introduction to Linear Algebra › Exercise 4.4.20
(a) True because Q T Q = I leads to ( Q − 1 ) ( Q − 1 ) = I .
(b) True. Q x = x 1 q 1 + x 2 q 2 . ∥ Q x ∥ 2 = x 1 2 + x 2 2 because q 1 ⋅ q 2 = 0 . Also ∥ Q x ∥ 2 = x T Q T Q x = x T x .
