Consider B = {1+ x,x + x²,1+ x²}, B' = {1+x²,1 – x²,1 – 2x}. i) Show that B and B' are bases for P2. ii) Find the coordinate matrices of p(x) = –x² + 4x + 7 relative to B and B' iii) Find the transition matrix PB¬B'· iv) Verify that [x(p)]g' = Pg¬g'[x(p)]g- %3D

Consider B = {1+ x,x + x²,1+ x²}, B' = {1+x²,1 – x²,1 – 2x}. i) Show that B and B' are bases for P2. ii) Find the coordinate matrices of p(x) = –x² + 4x + 7 relative to B and B' iii) Find the transition matrix PB¬B'· iv) Verify that [x(p)]g' = Pg¬g'[x(p)]g- %3D

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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Question

Consider
B = {1+x,x + x²,1 + x²},
B' = {1+x²,1 – x²,1 – 2x}.
i)
Show that B and B' are bases for P2.
ii)
Find the coordinate matrices of p(x) = -x² + 4x + 7 relative to B and B'
%3D
iii)
Find the transition matrix PB--B'-
iv)
Verify that [x(p)]g' = Pg¬g'[x(p)]g-

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