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Sorry, this question is making my head spin. Can someone help?

If x is an eigenvector for the square matrix A corresponding to eigenvalue 5, ie. if Ax = 5x, evaluate A^2x + 11Ax + 3x in terms of x.

Ax = 5x --->

A^2 x = (A A)x = A (A x) = A (5x) =
5 A x = 25 x

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