Question: need help with Linear Algebra (4) Great work! If you still have time, consider the following two challenging questions about how the transpose interact with

need help with Linear Algebra

(4) Great work! If you still have time, consider the following two challenging questions about how the transpose interact with eigenvalues and eigenvectors. Let A be an n x nmatrix. (a) Explain why A and AT have the same eigenvalues. (Hint: Compare the charac teristic polynomials of the two matrices.) (b) (Challenge question) Suppose that AT = A. Let A1, A2 be such that A1 a A2. Let x,y be such that Ax = Alx and Ay = by Check that x and y are orthogonal to each other

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