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 =U2find the matrix representation B-1of L with respect to the basis [u1, U2].

(1) Define the linear operator L by ℝ2 by three steps: For L(x), find scale x by 2, then rotate the…

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

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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