33 (a) (b) Let A(t) = = et 0 0 0 cos(t) sin(t) 0-sin(t) cos(t)) For any fixed tЄR, find det(A(t)). Show that the matrix A(t) is invertible for any tЄ R, and find the inverse (A(t))¹.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Question
33
(a)
(b)
Let
A(t) =
=
et
0
0
0 cos(t) sin(t)
0-sin(t) cos(t))
For any fixed tЄR, find det(A(t)).
Show that the matrix A(t) is invertible for any tЄ R, and find the
inverse (A(t))¹.
Transcribed Image Text:33 (a) (b) Let A(t) = = et 0 0 0 cos(t) sin(t) 0-sin(t) cos(t)) For any fixed tЄR, find det(A(t)). Show that the matrix A(t) is invertible for any tЄ R, and find the inverse (A(t))¹.
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