Question: Let A be the symmetric 3 x 3 matrix A = 2 -1 1 -1 1 2 -1 1 2 -- and u =

Let A be the symmetric 3 x 3 matrix A = 2

Let A be the symmetric 3 x 3 matrix A = 2 -1 1 -1 1 2 -1 1 2 -- and u = 1 You are given that the vectors u vectors of A. Use this information to find an orthonormal basis V, V2, V3 for R, where each vector v; is an eigenvector of A, and verify that A = \VV + AV2V + A3V3V3, where A1, A2, A3 are the eigenvalues of A. 2 are eigen- 1

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