Prove that if v is an eigenvector of A with eigenvalue and w is an eigenvector of A T with a different eigenvalue , then v and w are orthogonal vectors with respect to the dot product Illustrate this result when (i) (ii) A (2 1 3

Question: Prove that if v is an eigenvector of A with eigenvalue and w is an eigenvector of A T with a different eigenvalue

Prove that if v is an eigenvector of A with eigenvalue λ and w is an eigenvector of A^Twith a different eigenvalue μ ≠ λ, then v and w are orthogonal vectors with respect to the dot product. Illustrate this result when

(i)

A = (2 -1 3

(ii)

A = (2 -1 3

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