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Unformatted text preview: question is about the matrix âŽ¤ âŽ¡ âŽ¢ âŽ£ âˆ’ 1 A = âŽ¥ âŽ¦ 4 . (a) Find its eigenvalues and eigenvectors. âŽ¤ âŽ¡ Write the vector u (0) = âŽ¢ âŽ£ 2 âŽ¥ âŽ¦ as a combination of those eigenvectors. du (b) Solve the equation = Au starting with the same vector u (0) at time t = 0 . dt In other words: the solution u ( t ) is what combination of the eigenvectors of A ? (c) Find the 3 matrices in the Singular Value Decomposition A = U Î£ V T in two steps. â€“First, compute V and Î£ using the matrix A T A. â€“Second, Â±nd the (orthonormal) columns of U. MIT OpenCourseWare http://ocw.mit.edu 18.06 Linear Algebra Spring 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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 Fall '10
 Strang
 Linear Algebra, Algebra

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