a) Find the coordinate vector of x = of R³. To with respect to the ordered basis *- {0-1-8} E [x] E E = 2 -14 -88

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter3: Matrices
Section3.4: The Lu Factorization
Problem 16EQ
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(a) Find the coordinate vector of x =
of R³.
2
-4 with respect to the ordered basis
(b) Let F₁ be the ordered basis of R² given by
and let F2 be the ordered basis given by
*-(-E) 1-8}
2
P =
[x]E
=
E =
1
F₁
3
5-(2-0)
F₂:
-3
2
=
-14
-88
Find the transition matrix PF such that [x]F₂ = P₂<F₁ [X] F₁ for all x in R²:
[
= {[13].[2])}
5
1
Transcribed Image Text:(a) Find the coordinate vector of x = of R³. 2 -4 with respect to the ordered basis (b) Let F₁ be the ordered basis of R² given by and let F2 be the ordered basis given by *-(-E) 1-8} 2 P = [x]E = E = 1 F₁ 3 5-(2-0) F₂: -3 2 = -14 -88 Find the transition matrix PF such that [x]F₂ = P₂<F₁ [X] F₁ for all x in R²: [ = {[13].[2])} 5 1
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