Consider the matrix A = 1 1 P = Let x = 1 √2 1 √2 0 -|-~| 1 √6 1 Compute [x]. √6 2 √6 1/11/11/1 I 2 -1 -1 2 and D = " which can be orthogonally diagonalized A = PDPT, where 300 030 00 0 [] 3 . Let 3 be the basis for R³ given by the columns of P.

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