ame525_2011_hw3

ame525_2011_hw3 - AME525, Homework 3, Due: 09/28/11 in...

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Unformatted text preview: AME525, Homework 3, Due: 09/28/11 in class All steps must be shown for full credit. [Updated Sept 21/2011]. 1. Find a least-squares solution of A x = b for A = 1 1 1 1 1 1 1 1 1 1 1 1 , b = − 3 − 1 2 5 1 2. Find a least-squares solution of A x = b for A = 1 − 3 − 3 1 5 1 1 7 2 , b = 5 − 3 − 5 and compute the associated least-squares error, bardbl b − A ˆx bardbl . 3. Show that if A is a symmetric matrix, then A 2 is symmetric. 4. Show that if A is a orthogonally diagonalizable, then so is A 2 . 5. Find the singular values of the matrices in (a) and (b) (a) A = parenleftBigg 1 − 3 parenrightBigg (b) A = parenleftBigg √ 6 1 √ 6 parenrightBigg 6. [Problem 7.8 (10) in O’Neil 7th Edn.] Find the least squares line for the data: (-3,-7.4), (-1,-4.2), (0,-3.7), (2,-1.9), (4, 0.3), (7, 2.8), (11, 7.2) 1 7.7....
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This note was uploaded on 12/05/2011 for the course AME 525 taught by Professor Newton during the Spring '08 term at USC.

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ame525_2011_hw3 - AME525, Homework 3, Due: 09/28/11 in...

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