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Suppose that a matrix A has characteristic polynomial p(^) = 24 − 3a³ + 82² – 24. Consider the following statements. (i) A is a 3 x 3 matrix. (ii) That same p(2) is also the characteristic polynomial of A¯¹. (iii) = 2 is an eigenvalue of A. Determine which of the above statements are True (1) or False (2).

Suppose that a matrix A has characteristic polynomial p(^) = 24 − 3a³ + 82² – 24. Consider the following statements. (i) A is a 3 x 3 matrix. (ii) That same p(2) is also the characteristic polynomial of A¯¹. (iii) = 2 is an eigenvalue of A. Determine which of the above statements are True (1) or False (2).

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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Suppose that a matrix A has characteristic polynomial p(^) = 2ª − 3λ³ + 8λ² – 24. Consider the following statements. (i) A is a 3 x 3 matrix. (ii) That same p(2) is also the characteristic polynomial of A¯¹. (iii) 2 is an eigenvalue of A. Determine which of the above statements are True (1) or False (2).
Transcribed Image Text:Suppose that a matrix A has characteristic polynomial p(^) = 2ª − 3λ³ + 8λ² – 24. Consider the following statements. (i) A is a 3 x 3 matrix. (ii) That same p(2) is also the characteristic polynomial of A¯¹. (iii) 2 is an eigenvalue of A. Determine which of the above statements are True (1) or False (2).
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