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Matrix Question!eigenvectors and eigenvalues for symmetric matrix?

Suppose A is a symmetric N X N matrix with eigenvectors vi, i = 1; 2; 3 ...N with
corresponding eigenvalues ?i, i = 1; 2; 3 ...N.
Pick any two distinct eigenvalues (assuming such a pair exists). Let's call them ?1 and
?2 and their corresponding eigenvectors v1 and v2.
Write down the matrix equations that show that v1 and v2 are eigenvectors of A.
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