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ame525_2011_hw3

# ame525_2011_hw3 - AME525 Homework 3 Due in class All steps...

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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 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 , b = 3 1 0 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 0 0 3 parenrightBigg (b) A = parenleftBigg 6 1 0 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

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7. [Problem 8.6 (2) in O’Neil 7th Edn.] 8. [Problem 9.1 (2, 8, 14) in O’Neil 7th Edn.]
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