WINTER 2007 assign7-sol

WINTER 2007 assign7-sol - Math 235 Assignment 7 Due 9:15am...

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Unformatted text preview: Math 235 Assignment 7 Due 9:15am, Wednesday March 14, 2007. 1. From the Text § 6.4 #10. Find an orthogonal basis for the column space of the following matrix. - 1 6 6 3- 8 3 1- 2 6 1- 4- 3 Solution. Let x 1 = - 1 3 1 1 , x 2 = 6- 8- 2- 4 , x 3 = 6 3 6- 3 . We will use the Gram-Schmidt Process to find an orthogonal basis. v 1 = - 1 3 1 1 v 2 = x 2- x 2 · v 1 v 1 · v 1 v 1 = 6- 8- 2- 4 + 3 - 1 3 1 1 = 3 1 1- 1 v 3 = x 3- x 3 · v 1 v 1 · v 1 v 1- x 3 · v 2 v 2 · v 2 v 2 = 6 3 6- 3 - 1 2 - 1 3 1 1 - 5 2 3 1 1- 1 = - 1- 1 3- 1 The set - 1 3 1 1 , 3 1 1- 1 , - 1- 1 3- 1 forms an orthogonal basis for the above space. 1 #14. The columns of Q were obtained by applying the Gram-Shmidt process to the columns of A. Find an upper triangular matrix R such that A = QR. A = - 2 3 5 7 2- 2 4 6 , Q = - 2 7 5 7 5 7 2 7 2 7- 4 7 4 7 2 7 Solution....
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WINTER 2007 assign7-sol - Math 235 Assignment 7 Due 9:15am...

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