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

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section: Chapter Questions
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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 R3
O A
det (I + A) = 0
OB.
A=0is not an eigenvalue of A
OC.
Ax =Ax for every vector x in R
OD.
None of these statements is false
O E
Transcribed Image Text: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 R3 O A det (I + A) = 0 OB. A=0is not an eigenvalue of A OC. Ax =Ax for every vector x in R OD. None of these statements is false O E
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