(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 columnof A =Linalg_pdf.pdf= 1(9) The best least squares solution to the following (inconsistent) system of equations·is u =v =1and e=u +v = 025.3. PROBLEMS16725.3. Problems(1) Explain in detail how to use matrix methods to find the best (least squares) solution to= 1v = 1. Carry out the computationthe following (inconsistent) system of equationsyou 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 lineapproximation 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[11 -1A3=1 01 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 datadiffer most from the values your line predicts?

“Since you have asked multiple questions, we will solve the first question for you. If you want any…

Answered: (1) Explain in detail how to use matrix…

(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

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 32EQ

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Question

(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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