-3 (a) Find the coordinate vector of x = 2 with respect to the ordered basis 3 of R3: E= 0 -- {B· Q}· A]} -6 [x] E = (b) Let F₁ be the ordered basis of R2 given by F₁ = 3 and let F2 be the ordered basis given by 2 F2 = {[(3³}]} [6]} 2 Find the transition matrix PF+F₁ such that [x] F₂ = PF₁₂+F₁ [x] F₁ for all x in R²: P =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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-3
(a) Find the coordinate vector of x
=
2
with
respect to the ordered basis
3
of R3:
E=
0
-- {B· Q}· A]}
-6
[x] E =
(b) Let F₁ be the ordered basis of R2 given by
F₁ =
3
and let F2 be the ordered basis given by
2
F2
= {[(3³}]} [6]}
2
Find the transition matrix PF+F₁ such that [x] F₂ = PF₁₂+F₁ [x] F₁ for all x in R²:
P =
Transcribed Image Text:-3 (a) Find the coordinate vector of x = 2 with respect to the ordered basis 3 of R3: E= 0 -- {B· Q}· A]} -6 [x] E = (b) Let F₁ be the ordered basis of R2 given by F₁ = 3 and let F2 be the ordered basis given by 2 F2 = {[(3³}]} [6]} 2 Find the transition matrix PF+F₁ such that [x] F₂ = PF₁₂+F₁ [x] F₁ for all x in R²: P =
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