Unformatted text preview: . Summarize your conclusion about the impact of the third equation, as a function of Ç« , on the LS solution. 2. Fat systems: Consider Ë† i , Ë† j , Ë† k as unit vectors in the x , y and z directions. (a) Consider the fat (under-specifed) system Ax = b b 1 2 Ç« 2-1-Ç« B x y z = b 1-1 B with Ç« a very small number. (a) Identify span( A ) and null( A )? (b) What can you say about the solution space? 3. Singular Value Decomposition (SVD) Let A = b 1 1 1-1 1 B and Â²nd U , Î£ and V such that A = U Î£ V T . Repeat the process on A T . Use the fact that U = eig ( AA T ) âˆˆ R m Ã— m and V = eig ( A T A ) âˆˆ R n Ã— n , where eig ( S ) are the eigenvectors of a symmetric matrix S . Version 1.13 March 18, 2011 Ëœ /493/Assignments/HW #3b â€“ Version 1.13 March 18, 2011...
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- Spring '11
- Linear Algebra, Singular value decomposition, Orthogonal matrix, Univ. of Illinois