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a. Which of the following subspaces of U are invariant under D? (i). <1>, (ii). <1, a >, (iii). < COs a >, (iv). < cos a, sin a >.

a. Which of the following subspaces of U are invariant under D? (i). <1>, (ii). <1, a >, (iii). < COs a >, (iv). < cos a, sin a >.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...
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a. Which of the following subspaces of U are invariant under D? (i). <1>, (ii). <1, a >, (iii). < cos a>, (iv). < cos z, sin a>. b. Determine all 1-dimensional linear subspaces of U invariant under D.
Transcribed Image Text:a. Which of the following subspaces of U are invariant under D? (i). <1>, (ii). <1, a >, (iii). < cos a>, (iv). < cos z, sin a>. b. Determine all 1-dimensional linear subspaces of U invariant under D.
27 In the vector space of differentiable functions from R to R we consider the linear subspace U =< cos r, sin r, r, 1 >. The linear map D: U + U is given by differentiation: (Df)(r) = f'(x).
Transcribed Image Text:27 In the vector space of differentiable functions from R to R we consider the linear subspace U =< cos r, sin r, r, 1 >. The linear map D: U + U is given by differentiation: (Df)(r) = f'(x).
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