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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

Advanced Engineering Mathematics
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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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
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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