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1. Let A be an inevirtible m ine invertible matrix. and an eigenvalue of A. Prove, using the definition of an eigenvalue, that eigenvalue of A-1 is an $1(d_0_P)]=W!_k DEW 2. IF A is an invertible matrix that is diagonalisable, prove that A¹ is diagonalisable

1. Let A be an inevirtible m ine invertible matrix. and an eigenvalue of A. Prove, using the definition of an eigenvalue, that eigenvalue of A-1 is an $1(d_0_P)]=W!_k DEW 2. IF A is an invertible matrix that is diagonalisable, prove that A¹ is diagonalisable

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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Question pla 23 24 1. Let A be an inevirtible m ine invertible matrix and X an eigenvalue of A. Prove, using the definition of an eigenvalue, that eigenvalue of A is an Elt wede 2. IF A is an invertible matrix that is diagonalisable, prove that A¹ is diagonalisable HT
Transcribed Image Text:Question pla 23 24 1. Let A be an inevirtible m ine invertible matrix and X an eigenvalue of A. Prove, using the definition of an eigenvalue, that eigenvalue of A is an Elt wede 2. IF A is an invertible matrix that is diagonalisable, prove that A¹ is diagonalisable HT
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