Let T: R³ R2 be a linear mapping.→10*([:]) = [ ] ¹ ({]) - [ ] -~-~(:)) - [²7] ([])-T=and Tfind T(ED).Given that Tsin (a)Ərfα ΩE

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Answered: Let T: R³ R² be a linear mapping. 10…

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

Let T: R³ R2 be a linear mapping.
→
10
*([:]) = [ ] ¹ ({]) - [ ] -~-~(:)) - [²7] ([])
-
T
=
and T
find T
(ED).
Given that T
sin (a)
Ər
f
α Ω
E

Expert Solution

Step 1: Expanding the domain element:

$O n e space m a y space f i n d space t h a t space T open parentheses open square brackets table row 1 row 7 row 2 end table close square brackets close parentheses equals T open parentheses 1 open square brackets table row 1 row 0 row 0 end table close square brackets plus 7 open square brackets table row 0 row 1 row 0 end table close square brackets plus 2 open square brackets table row 0 row 0 row 1 end table close square brackets close parentheses equals T open parentheses open square brackets table row 1 row 0 row 0 end table close square brackets close parentheses plus 7 T open parentheses open square brackets table row 0 row 1 row 0 end table close square brackets close parentheses plus 2 T open parentheses open square brackets table row 0 row 0 row 1 end table close square brackets close parentheses comma space a s space T space i s space l i n e a r.$