Let TA : RR3 be multiplication by the orthogonal matrix123332A =321Find TA(x) for the vector x =33312- -- -333(3)?TA(x) =??Using the Euclidean inner product on R³, verify that ||TA(x)|| = ||x||.||TA(x)||:||x|||

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Let TA : R → R³ be multiplication by the orthogonal matrix 1 21 3 3 3 6- 1 Find TA(x) for the vector x = 3 A 3 - - 3 3 1 2 -- 3 3 ()- ? TA(x) = ? %3D ? Using the Euclidean inner product on R³, verify that ||TA(x)|| = ||x||. ||TA(x)|| = ||æ| : N|3

Let TA : R → R³ be multiplication by the orthogonal matrix 1 21 3 3 3 6- 1 Find TA(x) for the vector x = 3 A 3 - - 3 3 1 2 -- 3 3 ()- ? TA(x) = ? %3D ? Using the Euclidean inner product on R³, verify that ||TA(x)|| = ||x||. ||TA(x)|| = ||æ| : N|3

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 TA : R
R3 be multiplication by the orthogonal matrix
1
2
3
3
3
2
A =
3
2
1
Find TA(x) for the vector x =
3
3
3
1
2
- -
- -
3
3
3
(3)
?
TA(x) =
?
?
Using the Euclidean inner product on R³, verify that ||TA(x)|| = ||x||.
||TA(x)||:
||x||
|

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