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-1 4 and b = 1 2 Let A = (a) . 'Find the orthogonal projection of b onto Col A. Use your answer in part a to find the least squares solution to Ax = b. In particular, do (b) NOT use the normal equations since A has orthogonal columns. Use the weights on the basis vectors in order to find the least squares solution. (c) What is the least squares error in the approximation to the solution of Ax = b?

-1 4 and b = 1 2 Let A = (a) . 'Find the orthogonal projection of b onto Col A. Use your answer in part a to find the least squares solution to Ax = b. In particular, do (b) NOT use the normal equations since A has orthogonal columns. Use the weights on the basis vectors in order to find the least squares solution. (c) What is the least squares error in the approximation to the solution of Ax = b?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I am struggling to understand this concept without using normal equations.

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3. Let A= -1 4 andb= 1 2 (a) ' Find the orthogonal projection of b onto Col A. Use your answer in part a to find the least squares solution to Ax = b. In particular, do (b) NOT use the normal equations since A has orthogonal columns. Use the weights on the basis vectors in order to find the least squares solution. (c) What is the least squares error in the approximation to the solution of Ax = b?
Transcribed Image Text:3. Let A= -1 4 andb= 1 2 (a) ' Find the orthogonal projection of b onto Col A. Use your answer in part a to find the least squares solution to Ax = b. In particular, do (b) NOT use the normal equations since A has orthogonal columns. Use the weights on the basis vectors in order to find the least squares solution. (c) What is the least squares error in the approximation to the solution of Ax = b?
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