Let a : V → V be a diagonalisable linear map where V is a vector space of dimension 4 over the field F3. (a) Is it possible for ma (x) to have degree 4? (b) Is it possible for ma(x) to have degree 3? Select one: Yes to both There is not enough information as it depends on the linear map in question. (a) Yes (b) No O(a) No (b) Yes No to both

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.4: Spanning Sets And Linear Independence
Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...
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Let a : V → V be a diagonalisable linear map where V is a vector space of dimension 4 over the field F3.
(a) Is it possible for ma (x) to have degree 4?
(b) Is it possible for ma(x) to have degree 3?
Select one:
Yes to both
There is not enough information as it depends on the linear map in question.
(a) Yes (b) No
O (a) No (b) Yes
No to both
Transcribed Image Text:Let a : V → V be a diagonalisable linear map where V is a vector space of dimension 4 over the field F3. (a) Is it possible for ma (x) to have degree 4? (b) Is it possible for ma(x) to have degree 3? Select one: Yes to both There is not enough information as it depends on the linear map in question. (a) Yes (b) No O (a) No (b) Yes No to both
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