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# Linear Algebra-Homework 9 March 1, 2012 All problems are from textbook, Section 5.2 Problem 1 (problems 2, 3, 4, 13, 14, 9) Use the Graham-Schmidt...

Can you solve problem 1 part 3?
Linear Algebra-Homework 9 March 1, 2012 All problems are from textbook, Section 5.2 Problem 1 (problems 2, 3, 4, 13, 14, 9) Use the Graham-Schmidt process to ﬁnd an orthonormal basis for the vector space V in the following cases: 1. V has basis 6 3 6 , 2 - 6 3 2. V has basis 4 0 3 , 25 0 - 25 3. V has basis 4 0 3 , 25 0 - 25 , 0 - 2 0 4. V has basis 1 1 1 1 , 1 0 0 1 , 0 2 1 - 1 5. V has basis 1 7 1 7 , 0 7 2 7 , 1 8 1 6 6. V has basis 1 1 1 1 , 1 9 - 5 3 Problem 2 (problem 32) Find an orthonormal basis for the plane x 1 + x 2 + x 3 = 0 . Problem 3 (problem 33) Find an orthonormal basis of the kernel of the linear transformation T : R 4 R 2 given by T a b c d = ± 1 1 1 1 1 - 1 - 1 1 ² a b c d . 1
Problem 4 (problem 34) Find an orthonormal basis for the image space of the linear transformation T : R 4 R 2 given by T a b c d = ± 1 1 1 1 1 2 3 4 ² a b c d Problem 5 (problem 35) Find an orthonormal basis for the image of the linear transformation T : R 3 R 3 given by: T a b c = 1 2 1 2 1 1 1 1 0 a b c 2
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Gram Schmidt Orthogonalization 4
25
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Given the vectors,a = 0, b = 0 &amp; c = −2, we have as follows for
3
−25
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creating a orthonormal basis v1 v2 v3
1. Generate Orthogonal Vectors: We have...

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