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1' 12. Let A = 1 3 and b: a. Find the least squares solution to Ax = b. b. Determine whether the least squares solution found in part (a) is a solution to Ax = b. 13. The data (1,-3), (2,1) and (3,2) is gathered as nart

1' 12. Let A = 1 3 and b: a. Find the least squares solution to Ax = b. b. Determine whether the least squares solution found in part (a) is a solution to Ax = b. 13. The data (1,-3), (2,1) and (3,2) is gathered as nart

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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Question 12
1 1 1 1 3 12. Let A = and b = a. Find the least squares solution to Ax = b. b. Determine whether the least squares solution found in part (a) is a solution to Ax = b. 13. The data (1,–3), (2,1) and (3,2) is gathered as part of an experiment. Find the line of best least squares fit for this data, and then use this line to approximate the value of y associated with x = 5/2. 14. Give an interpolating polynomial of degree 2 for the data given in problem 13. 15. Use elementary row operations to find the inverse of the matrix-1 1 0 -1 16. Let V = span a. Find all vectors v E V with length 1. b. Use the Gram-Schmidt process to find an orthogonal basis for V. 17. The data (-1,4), (0,2), (2,-3), (4, -3) and (7,4) was gathered as part of an experiment. a. Plot this data. b. Set up a system of equations that can be solved to find the values a, b and c so that y = a + bx + cx2 is the best least squares fit for this data. Do not solve the system. 18. Define the function T: P2 - P2 via T(g(x)) = (2x2-1)g'(x) + g(x). MacBook Pro DII DD 80 FB F6 F7 F9 F10 F12 F4 %24 8. 9. %3D 4 5 6 R Y U J K L V lt .. .. V エ B
Transcribed Image Text:1 1 1 1 3 12. Let A = and b = a. Find the least squares solution to Ax = b. b. Determine whether the least squares solution found in part (a) is a solution to Ax = b. 13. The data (1,–3), (2,1) and (3,2) is gathered as part of an experiment. Find the line of best least squares fit for this data, and then use this line to approximate the value of y associated with x = 5/2. 14. Give an interpolating polynomial of degree 2 for the data given in problem 13. 15. Use elementary row operations to find the inverse of the matrix-1 1 0 -1 16. Let V = span a. Find all vectors v E V with length 1. b. Use the Gram-Schmidt process to find an orthogonal basis for V. 17. The data (-1,4), (0,2), (2,-3), (4, -3) and (7,4) was gathered as part of an experiment. a. Plot this data. b. Set up a system of equations that can be solved to find the values a, b and c so that y = a + bx + cx2 is the best least squares fit for this data. Do not solve the system. 18. Define the function T: P2 - P2 via T(g(x)) = (2x2-1)g'(x) + g(x). MacBook Pro DII DD 80 FB F6 F7 F9 F10 F12 F4 %24 8. 9. %3D 4 5 6 R Y U J K L V lt .. .. V エ B
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