In this question, pA(x) denotes the characteristic polynomial of an n × n matrix A and mA(x) denotes its minimal polynomial. (a)  Working over R, find pA(x) and mA(x) for       0 2 4 A= 4 2 0       0 0 3 , which is a 3x3 matrix  (b)  Can the matrix in part (a) be diagonalised over R? Justify your answer.  (c)  Repeat parts (a) and (b) with R replaced by F5

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 30E
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 In this question, pA(x) denotes the characteristic polynomial of an n × n matrix A and mA(x) denotes its minimal polynomial.

  1. (a)  Working over R, find pA(x) and mA(x) for

          0 2 4
    A= 4 2 0
          0 0 3 , which is a 3x3 matrix 

    (b)  Can the matrix in part (a) be diagonalised over R? Justify your answer. 
    (c)  Repeat parts (a) and (b) with R replaced by F5
In this question, PA(x) denotes the characteristic
polynomial of an n x n matrix A and m₁(x) denotes its minimal polynomial.
(a) Working over R, find pÂ(x) and m₁(x) for
A =
=
024
420
003
(b) Can the matrix in part (a) be diagonalised over R? Justify your answer.
(c) Repeat parts (a) and (b) with R replaced by F5
Transcribed Image Text:In this question, PA(x) denotes the characteristic polynomial of an n x n matrix A and m₁(x) denotes its minimal polynomial. (a) Working over R, find pÂ(x) and m₁(x) for A = = 024 420 003 (b) Can the matrix in part (a) be diagonalised over R? Justify your answer. (c) Repeat parts (a) and (b) with R replaced by F5
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