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(1) Explain in detail how to use matrix methods to find the best (least squares) solution to = 1 the following (inconsistent) system of equations you describe. = 1. Carry out the computation

(1) Explain in detail how to use matrix methods to find the best (least squares) solution to = 1 the following (inconsistent) system of equations you describe. = 1. Carry out the computation

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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(8) Co5l O Mowing data: y = 4 at t = -1; y = 5 at t = 0; y = 9 at t 1 61 I 00:42 (a) Then the best (least squares) line which fits the data is y = c+ dt where c= and d= (b), The orthogonal projection of b = (4,5, 9) onto the column of A = Linalg_pdf.pdf = 1 (9) The best least squares solution to the following (inconsistent) system of equations· is u = v =1 and e= u +v = 0 25.3. PROBLEMS 167 25.3. Problems (1) Explain in detail how to use matrix methods to find the best (least squares) solution to = 1 v = 1. Carry out the computation the following (inconsistent) system of equations you describe, u+v = 0 (2) The following data y are observed at times t: y = 4 when t = -2; y = 3 when t = -1; = 1 when t = 0; and y = 0 when t = 2. (a) Explain how to use matrix methods to find the best (least squares) straight line approximation to the data. Carry out the computation you describe. (b) Find the orthogonal projection of y = (4, 3, 1,0) on the column space of the matrix [1 1 -1 A3= 1 0 1 2 (c) Explain carefully what your answer in (b) has to do with part (a). (d) At what time does the largest error occur? That is, when does the observed data differ most from the values your line predicts?
Transcribed Image Text:(8) Co5l O Mowing data: y = 4 at t = -1; y = 5 at t = 0; y = 9 at t 1 61 I 00:42 (a) Then the best (least squares) line which fits the data is y = c+ dt where c= and d= (b), The orthogonal projection of b = (4,5, 9) onto the column of A = Linalg_pdf.pdf = 1 (9) The best least squares solution to the following (inconsistent) system of equations· is u = v =1 and e= u +v = 0 25.3. PROBLEMS 167 25.3. Problems (1) Explain in detail how to use matrix methods to find the best (least squares) solution to = 1 v = 1. Carry out the computation the following (inconsistent) system of equations you describe, u+v = 0 (2) The following data y are observed at times t: y = 4 when t = -2; y = 3 when t = -1; = 1 when t = 0; and y = 0 when t = 2. (a) Explain how to use matrix methods to find the best (least squares) straight line approximation to the data. Carry out the computation you describe. (b) Find the orthogonal projection of y = (4, 3, 1,0) on the column space of the matrix [1 1 -1 A3= 1 0 1 2 (c) Explain carefully what your answer in (b) has to do with part (a). (d) At what time does the largest error occur? That is, when does the observed data differ most from the values your line predicts?
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