Answered: 0 -1 6. 2 Find the least squares… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 71E

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1.Assume (f,g) = | f(x)g(x)dx is the inner product for V = P, . Apply the Gram-Schmidt process to
orthonormalize the basis B = {1,x, x}.
%3D
1
-1
6.
2 1 -2
2 Find the least squares solution for Axr =b where A =
1
; b=
9.
1
1 -1

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The normal equations for a least-squares line y = Bo + Bix may be written in the form nBo + Bi Ix = Ev Bo Ex + Bi I x? = Exy (7) 15. Derive the normal equations (7) from the matrix form given in this section.
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Consider the quadratic form Q(x, y) = -² A = la cla 14 9 ala 10 Ila 28 9 ---/- 14 9 14 9 14 9 20 9 56 x y 9 following principal minors of the matrix A: The (leading) principal minor 1pm3 = pm3 of order 3: The leading principal minor 1pm² = pm3 of order 2: The leading principal minor 1pm₁ = pm of order 1: The principal minor pm² of order 2: The principal minor pm² of order 2: The principal minor pm of order 1: The principal minor pm of order 1: 9 Now use your answers to classify Q: (No answer given) -28 x z We want to classify this using Sylvester's Criteria (the principal minor test). Calculate the 28 y z 9 + 202² with symmetric coefficient matrix
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