2. Please provide a step-by-step proof that outlines and and all definitions or theorems that were used to solve the problem without skipping steps. 13%3D2.nowConsioler He ondeved besis B for R3 aud veetors ū aud waiven above. Let T R?->K be a einear function so thatTEV.)= -, TCVE)=Vg ++ TCV3) =Ù, where el is given instaudard coordinates,Ca) Tue staudared coordinates of the vector VeR sothat [♡]a= is%3D2.(6) The matrua of T with respect to te basis B is1.ce) Let ę-ge,êz,e &R. The chauge of coorolinate8 'matrie from B-coordinatesinto -oordinates isbe til studared ordered basisGiven the above results, ansuer vere question belowC.Owithout performing aury adolitional computations, find thematrix A of T with respect to the stoudard basis of R.(That is find A=[T]g).You do not need to Simplifny.

Answered: Image /qna-images/answer/7be4e848-3cd0-4ffe-a741-094983bb08cb.jpg

B = wこ nov Considler He ondered basis B Por R3 aud veetors ù given albove. Let T.R?→R be a einear function so that aud w TEV.)= -Ì, TeVe)=Ts + TC =, where el is given in stoudard coordinates, Ca) The staudared coordinates of the vector Jee +hat [v]e=あs So C6) The matrda eof T witn respect to the basis B is ce) Let E- ề, Ege} be the staudared orelered basis f R. The chauge of coorolinates matrie from B-coordinates into 0ordinates is Given the above results, ansuer vere question below! O without performing auny adolitional computations, find the matrix A of T with respect to the stoudard basis ofR. CThat is find A=[T]g.).You do not need to SimplifrA.

B = wこ nov Considler He ondered basis B Por R3 aud veetors ù given albove. Let T.R?→R be a einear function so that aud w TEV.)= -Ì, TeVe)=Ts + TC =, where el is given in stoudard coordinates, Ca) The staudared coordinates of the vector Jee +hat [v]e=あs So C6) The matrda eof T witn respect to the basis B is ce) Let E- ề, Ege} be the staudared orelered basis f R. The chauge of coorolinates matrie from B-coordinates into 0ordinates is Given the above results, ansuer vere question below! O without performing auny adolitional computations, find the matrix A of T with respect to the stoudard basis ofR. CThat is find A=[T]g.).You do not need to SimplifrA.

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

2. Please provide a step-by-step proof that outlines and and all definitions or theorems that were used to solve the problem without skipping steps.

13
%3D
2.
now
Consioler He ondeved besis B for R3 aud veetors ū aud w
aiven above. Let T R?->K be a einear function so that
TEV.)= -, TCVE)=Vg +
+ TCV3) =Ù, where el is given in
staudard coordinates,
Ca) Tue staudared coordinates of the vector VeR so
that [♡]a= is
%3D
2.
(6) The matrua of T with respect to te basis B is
1.
ce) Let ę-ge,êz,e &
R. The chauge of coorolinate8 'matrie from B-coordinates
into -oordinates is
be til studared ordered basis
Given the above results, ansuer vere question below
C.
Owithout performing aury adolitional computations, find the
matrix A of T with respect to the stoudard basis of R.
(That is find A=[T]g).You do not need to Simplifny.

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