Let A = 2 1 29 2 36 and let W= COICA). Find on orthonormal basis for W. . Find a basis of W. Set up (but do not solve) a matrix equation to find the parabola yax² + bx + C that best fits the data {(1,2), (-1,3), (4,1), (5,2), (7-3) { in the least-squares sense. Do not multiply out, invert, or row-reduce any matrices.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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1. a)
Let A = 2
1
2 9
-1
2
36
and let W= C01CA).
Find on orthonormal basis for Wi
ii. Find a basis of W.
b) Set up (but do not solve) a matrix equation to find
the parabola y = ax² + bx + C that best fits the data
{(1;2), (-1,3), (4,1), (5,2), (7,-3) { in the least-squares
sense. Do not multiply out, invert, or row-reduce any
matrices.
Transcribed Image Text:1. a) Let A = 2 1 2 9 -1 2 36 and let W= C01CA). Find on orthonormal basis for Wi ii. Find a basis of W. b) Set up (but do not solve) a matrix equation to find the parabola y = ax² + bx + C that best fits the data {(1;2), (-1,3), (4,1), (5,2), (7,-3) { in the least-squares sense. Do not multiply out, invert, or row-reduce any matrices.
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