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
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
Section8.4: Zeros Of A Polynomial
Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0de9773e-39c1-4df6-a7d6-864501c7f552%2F738e455c-a9c8-49b8-baff-77e2aa25243d%2Fw5q1ao_processed.png&w=3840&q=75)
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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