MATH221 April 2009
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Find a formula for , where You may leave your ﬁnal answer as a product of three matrices.
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
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To find a formula for , we first need to find matrices P and D such that , where D is a diagonal matrix, whose diagonal entries are eigenvalues of A, and their corresponding eigenvectors are the columns of the matrix P.
So we have , , and