3- I want solution of this question with all steps, please. Thanks Given the (2 x 2) orthogonal matrix, T(0), find T2 and compare the resultwith T(20). Using this information, find T ).36[cos 0 - sin 0where T(0) =Lsin 0cos 03.

Given matrix is: Tθ=cosθ-sinθsinθcosθ To find the T2:…

Answered: Given the (2 x 2) orthogonal matrix,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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3- I want solution of this question with all steps, please. Thanks

Given the (2 x 2) orthogonal matrix, T(0), find T2 and compare the result
with T(20). Using this information, find T ).
36
[cos 0 - sin 0
where T(0) =
Lsin 0
cos 0
3.

Expert Solution

Step 1

Given matrix is:

$T (θ) = [\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix}]$

To find the $T^{2}$ :

$T (θ) \times T (θ) = [\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix}] \times [\begin{matrix} \cos (θ) & - \sin (θ) \\ \sin (θ) & \cos (θ) \end{matrix}] T^{2} = [\begin{matrix} \cos (θ) \cdot \cos (θ) + (- \sin (θ) \cdot \sin (θ)) & - \cos (θ) \sin (θ) - \sin (θ) \cos (θ) \\ \sin (θ) \cdot \cos (θ) + \sin (θ) \cdot \cos (θ) & - \sin (θ) \sin (θ) + \cos (θ) \cdot \cos (θ) \end{matrix}] T^{2} = [\begin{matrix} \cos (2 θ) & - \sin (2 θ) \\ \sin (2 θ) & \cos (2 θ) \end{matrix}] . . . . . . . . . . . . . . . . . . . . . . . . (1)$

For $T (2 θ)$ put $2 θ$ in given matrix:

$T (2 θ) = [\begin{matrix} \cos (2 θ) & - \sin (2 θ) \\ \sin (2 θ) & \cos (2 θ) \end{matrix}] . . . . . . . . . . . (2)$

From equation (1) and (2):

$T^{2} = T (2 θ)$

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