Question: 3. Let x, y E R be two nonzero vectors such that |x|2 = y |2. Assume x x y and let u = X-y

3. Let x, y E R" be two nonzero vectors such that |x|2 = y |2. Assume x x y and let u = X-y x-yl/2 (a) Prove that uu x = -uu' y (b) Prove that (I - uu )x = (I - uu] )y. (c) Using (a) and (b), prove that the Householder matrix H = I-2uu satisfies Hx = y and Hy = x

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