solutions4bd

solutions4bd - Math 33a/2, Quiz 4bd, November 8, 2007 Name:...

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Math 33a/2, Quiz 4bd, November 8, 2007 Name: UCLA ID: 1. Find an orthonormal basis for the subspace V of R 4 , where V = ker ± 1 0 4 - 3 0 1 2 - 1 ² . Solution. The matrix ± 1 0 4 - 3 0 1 2 - 1 ² is already in rref, so we can easily write down a basis for its kernel: ~v 1 = - 4 - 2 1 0 , ~v 2 = 3 1 0 1 . To find an orthonormal basis { ~u 1 , ~u 2 } for this space, we apply the Gram-Schmidt process. ~u 1 = ~v 1 || ~v 1 || = 1 21 - 4 - 2 1 0 . To obtain ~u 2 , we take ~v 2 - ( ~v 2 · ~u 1 ) ~u 1 and divide by its length. ~v 2 - ( ~v 2 · ~u 1 ) = 3 1 0 1 - ( 3 1 0 1 · 1 21 - 4 - 2 1 0
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This note was uploaded on 04/02/2008 for the course MATH 33a taught by Professor Lee during the Fall '08 term at UCLA.

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