Let A be a symmetric matrix (that is, A = AT) with distinct eigenvalues λ1 and λ2. For such a matrix, if v1 and v2 are eigenvectors belonging to the distinct eigenvalues λ1 and λ2, respectively, then v1 and v2 are orthogonal
(a) Illustrate this for

(b) Prove fact for an n × n symmetric matrix. Use the fact that v1. v2 = v1Tv2 (as a matrix product).

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