Let A be the symmetric 3 x 3 matrix A = 2 -1 1 -1 1...

Transcribed Image Text:

Let A be the symmetric 3 x 3 matrix A = 2 -1 1 -1 1 2 -1 −1 2 -- and u₂ = 1 You are given that the vectors u₁ vectors of A. Use this information to find an orthonormal basis V₁, V2, V3 for R³, where each vector v; is an eigenvector of A, and verify that A = \₁V₁V₁ + A₂V2V½ + A3V3V3, where A1, A2, A3 are the eigenvalues of A. 2 are eigen- 1 Let A be the symmetric 3 x 3 matrix A = 2 -1 1 -1 1 2 -1 −1 2 -- and u₂ = 1 You are given that the vectors u₁ vectors of A. Use this information to find an orthonormal basis V₁, V2, V3 for R³, where each vector v; is an eigenvector of A, and verify that A = \₁V₁V₁ + A₂V2V½ + A3V3V3, where A1, A2, A3 are the eigenvalues of A. 2 are eigen- 1