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29 Jan 2022
Let A = (s t t s), where s and t are any real numbers. (a) Verify that A has real eigenvalues. (b) For what s and t the eigenvalues are not distinct? (c) Show that there exist two linearly independent eigenvectors that are perpendicular to each other (u and v are perpendicular if the dot product u^T v = 0).
Let A = (s t t s), where s and t are any real numbers. (a) Verify that A has real eigenvalues. (b) For what s and t the eigenvalues are not distinct? (c) Show that there exist two linearly independent eigenvectors that are perpendicular to each other (u and v are perpendicular if the dot product u^T v = 0).
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