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Unformatted text preview: question is about the matrix 1 A = 4 . (a) Find its eigenvalues and eigenvectors. Write the vector u (0) = 2 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 V T in two steps. First, compute V and using the matrix A T A. Second, 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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This note was uploaded on 08/22/2011 for the course MATH 1806 taught by Professor Strang during the Fall '10 term at MIT.
 Fall '10
 Strang
 Linear Algebra, Algebra

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