|aProve that the matrix A =is diagonalizable if –4bc < (a–-d)? and is not8.a)diagonalizable if –4bc > (a – d)².What happens when –4bc = (a –d)² ?b)Give an example of a 3 × 3 matrix that you know is not diagonalizable and explain why thisis so.

Answered: a) Prove that the matrix A = is…

a) Prove that the matrix A = is diagonalizable if –4bc < с d diagonalizable if –4bc > (a– d)². What happens when –4bc = (a– d)² ?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.5: Subspaces, Basis, Dimension, And Rank

Problem 63EQ

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Question

|a
Prove that the matrix A =
is diagonalizable if –4bc < (a–
-d)? and is not
8.
a)
diagonalizable if –4bc > (a – d)².
What happens when –4bc = (a –d)² ?
b)
Give an example of a 3 × 3 matrix that you know is not diagonalizable and explain why this
is so.

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