%3D Considler the ordered bsis B for K and vectors ù labove. Let T:R>E bie a linear functon so that 上G)=-aって()-i +TCJ- ere ūisgiueu in standard Coordinates. cawhat are te standard coordinates of the vector ER So that エl-? given. [T]e (6) Compute CNote that if T:V>V is ai Linear transformation and ß is a basis for V, then we write [T] = [TIg.) LTJ, the matrix d T with respect to the basis B. Let =E, be the staudard basis & R Find tee chauge-of-coordinates matrie from B-coordinates into E-coordinates.
%3D Considler the ordered bsis B for K and vectors ù labove. Let T:R>E bie a linear functon so that 上G)=-aって()-i +TCJ- ere ūisgiueu in standard Coordinates. cawhat are te standard coordinates of the vector ER So that エl-? given. [T]e (6) Compute CNote that if T:V>V is ai Linear transformation and ß is a basis for V, then we write [T] = [TIg.) LTJ, the matrix d T with respect to the basis B. Let =E, be the staudard basis & R Find tee chauge-of-coordinates matrie from B-coordinates into E-coordinates.
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
Two (a-d). Provide a detailed proof that covers any definitions/theoremsused to solve the problem without skipping steps.
Transcribed Image Text:iー12
%3D
%3D
Consider thee ordered bosis B for K and vectors ù 3 Ù aiven
above.Let T:PR>R be a linear functon so that
TG)=- T(=Vs +T T=ū, where is giueu in
standaird Coordinates.
(awhat are Kee standard coordinates of the vector TER so that
%3D
(6) Compote LTIB, the matrix dT with respect to the basis B.
(Note that if T:V>V is a Linear transformatiom and B is
a basis for V, then wewrite [T = [Td8.)
%3D
a
Let ={è s be the staudard basis & R Find teee
chauge-of-coordinates matrie from B-coordinates into
%3D
E-coordinates.
cD without performing auy
matrix A of T with resspect to tue staudard bosis of R.
cThat is, find A=LTde.):You olo not need to simplify
odditional
computations, find te
your auswer.
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