1. Define the linear operator L on R² by three steps: For L(x), first scale x by v2, then rotate the result counter-clockwise by 45° = 7/4 radians, finally reflect that result across the (horizontal) x1 axis. (Hint: cos(7/4) = sin(r/4) = 1/v/2.] (a) Find the standard matrix representation A of operator L (by columns is easiest). (:). (;) (b) Use your A to find L(x) where x 3 (c) Given the basis find the matrix representation B U2 = of L with respect to the basis [u1, u2].
1. Define the linear operator L on R² by three steps: For L(x), first scale x by v2, then rotate the result counter-clockwise by 45° = 7/4 radians, finally reflect that result across the (horizontal) x1 axis. (Hint: cos(7/4) = sin(r/4) = 1/v/2.] (a) Find the standard matrix representation A of operator L (by columns is easiest). (:). (;) (b) Use your A to find L(x) where x 3 (c) Given the basis find the matrix representation B U2 = of L with respect to the basis [u1, u2].
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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![1. Define the linear operator L on R² by three steps:
For L(x), first scale x by v2,
then rotate the result counter-clockwise by 45° = T/4 radians,
finally reflect that result across the (horizontal) x1 axis.
[Hint: cos(7/4) = sin(7/4) = 1//2.]
(a) Find the standard matrix representation A of operator L (by columns is easiest).
(:)
()
(b) Use your A to find L(x) where x =
1
(c) Given the basis uj =
U2
find the matrix representation B
-1
of L with respect to the basis [u1, U2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d14a18-18b6-4b9f-91b0-8c8acc9b34e2%2F1e86bc3a-900b-4622-96da-7fc0b72f2e2c%2Fdon9hu_processed.png&w=3840&q=75)
Transcribed Image Text:1. Define the linear operator L on R² by three steps:
For L(x), first scale x by v2,
then rotate the result counter-clockwise by 45° = T/4 radians,
finally reflect that result across the (horizontal) x1 axis.
[Hint: cos(7/4) = sin(7/4) = 1//2.]
(a) Find the standard matrix representation A of operator L (by columns is easiest).
(:)
()
(b) Use your A to find L(x) where x =
1
(c) Given the basis uj =
U2
find the matrix representation B
-1
of L with respect to the basis [u1, U2].
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