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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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||
|
Transcribed Image Text: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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