(b) Check whether the distributions D, and D2 are integrable:(i) D, on R' is spanned by the following vector fieldsZ =+I1W =(ii) D2 on the special linear group SI(R) = {A € M2x2: det(A) = 1}: R → R' isgenerated by%3Dcos 0sin 0 cos esin 0U =V =

Answered: Image /qna-images/answer/c0d38624-77ca-455b-bf7e-61a7c1e55ce2.jpg

(b) Check whether the distributions D1 and D2 are integrable: (i) Di on R° is spanned by the following vector ficlds W = I3 (ii) D2 on the special linear group SL2(R) = {A € M2x2: det(A) = 1} : R R* is generated by %3D -) v-( ) cos 0 sin 0 U = V = -sin 0 cos e

(b) Check whether the distributions D1 and D2 are integrable: (i) Di on R° is spanned by the following vector ficlds W = I3 (ii) D2 on the special linear group SL2(R) = {A € M2x2: det(A) = 1} : R R* is generated by %3D -) v-( ) cos 0 sin 0 U = V = -sin 0 cos e

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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Question

(b) Check whether the distributions D, and D2 are integrable:
(i) D, on R' is spanned by the following vector fields
Z =
+I1
W =
(ii) D2 on the special linear group SI(R) = {A € M2x2: det(A) = 1}: R → R' is
generated by
%3D
cos 0
sin 0 cos e
sin 0
U =
V =

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