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
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.
-
(a) Working over R, find pA(x) and mA(x) for
0 2 4
(b) Can the matrix in part (a) be diagonalised over R? Justify your answer.
A= 4 2 0
0 0 3 , which is a 3x3 matrix
(c) Repeat parts (a) and (b) with R replaced by F5
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