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1. Let a e R and y E R be two nonzero vectors. (a) Find a Householder matrix H such that Hx = ay for

1. Let a e R" and y E R" be two nonzero vectors. (a) Find a Householder matrix H such that Hx = ay for some a > 0. (b) Prove that H found in (a) satisfies Hy = Ba for some B > 0

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