Let A be a diagonalizable 3x3 mat rix with P-AP=-I , where I is the identity mat rix. Which of the following statements is FALSE? Ax =-X for every vector x in R O A A2x = Ax for every vector x in R3 OB. None of these statements is false A=0is not an eigenvalue of A OD. det (I + A) = 0

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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Question 12
Let A be a diagonalizable 3x3 mat rix with
p-lAP=-I , where I is the identity mat rix.
Which of the following statements is FALSE?
Ax =-X for every vector x in R3
O A.
A2x =Ax for every vector x in R
OB.
None of these stat ements is false
A=0is not an eigenvalue of A
OD
det (I + A) = 0
OE.
A Click Submit to complete this assessment.
25
Transcribed Image Text:Question 12 Let A be a diagonalizable 3x3 mat rix with p-lAP=-I , where I is the identity mat rix. Which of the following statements is FALSE? Ax =-X for every vector x in R3 O A. A2x =Ax for every vector x in R OB. None of these stat ements is false A=0is not an eigenvalue of A OD det (I + A) = 0 OE. A Click Submit to complete this assessment. 25
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