Let A be a diagonalizable 3×3 mat rixwith P-'AP= -I,where I is the identity mat rix. Which of the following statements isFALSE? The equation Ax = -x has infinitely many solutions OA. None of these statementsis false. OB. det (AI – A) =(A +1)3 OC. A = 0is an eigenvalue of A OD. A-1= -I

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question 2
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?
The equation Ax = -x has infinitely many solutions
None of these statementsis false.
det (AI – A) =(A + 1)3
-
A = 0 is an eigenvalue of A
O D
A-1= -I
O E
Transcribed Image Text:Question 2 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? The equation Ax = -x has infinitely many solutions None of these statementsis false. det (AI – A) =(A + 1)3 - A = 0 is an eigenvalue of A O D A-1= -I O E
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