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Let A be a diagonalizable matrix, with characteristic polynomial det(AI – A) = (A – c)" for some constant c E R. Prove that A = cI, where I is the n × n identity matrix. ght Morte Mona Jonash Univer Universi 202 2021. sable task ersit 2021

Let A be a diagonalizable matrix, with characteristic polynomial det(AI – A) = (A – c)" for some constant c E R. Prove that A = cI, where I is the n × n identity matrix. ght Morte Mona Jonash Univer Universi 202 2021. sable task ersit 2021

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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4. Let A be a diagonalizable matrix, with characteristic polynomial det (AI – A) = (A – c)" for some constant c E R. Prove that A = cI, where I is the n x n identity matrix. Mo Mona Jonash Univ Univer niversi jversity rsity 2021 2021 2021 task ask
Transcribed Image Text:4. Let A be a diagonalizable matrix, with characteristic polynomial det (AI – A) = (A – c)" for some constant c E R. Prove that A = cI, where I is the n x n identity matrix. Mo Mona Jonash Univ Univer niversi jversity rsity 2021 2021 2021 task ask
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