Find the minimal polynomial m₁(x) of A = Is A diagonalisable over this field? Select one: 1 2 3 3 1 2 working over the field F5. 2 1 3 m₁(x) = (x + 1)(4+x+x²). Hence A is not diagonalisable. m₁(x) = x + 1. Hence A is diagonalisable. m₁(x) = (x+3)²(x + 4). Hence A is not diagonalisable. m₁(x) = (x + 1)(x + 2). Hence A is diagonalisable. None of the others apply

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 13E
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2 3
Find the minimal polynomial m₁(x) of A = 3 1 2 working over the field F5.
2 1 3
Is A diagonalisable over this field?
Select one:
m₁(x) = (x + 1)(4+x+x²). Hence A is not diagonalisable.
m₁(x) = x + 1. Hence A is diagonalisable.
m₁(x) = (x+3)²(x + 4). Hence A is not diagonalisable.
m₁(x) = (x + 1)(x + 2). Hence A is diagonalisable.
None of the others apply
Transcribed Image Text:1 2 3 Find the minimal polynomial m₁(x) of A = 3 1 2 working over the field F5. 2 1 3 Is A diagonalisable over this field? Select one: m₁(x) = (x + 1)(4+x+x²). Hence A is not diagonalisable. m₁(x) = x + 1. Hence A is diagonalisable. m₁(x) = (x+3)²(x + 4). Hence A is not diagonalisable. m₁(x) = (x + 1)(x + 2). Hence A is diagonalisable. None of the others apply
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