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Let A=
[7 -4 4]
[-4 5 0]
[4 0 9]

a) Orthogonally diagonalize A

b) Use answer from a) to construct a spectral decomposition for A.

c) Suppose that x=[1 2 1] and let u be the eigen vector from a) corresponding to the largest eigen-value of A. If W=Span {u}, then use b) to decompose x into a sum of vectors, one in W and the other in W¡Í.

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