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Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ +62² 15. Consider the following statements. (1) λ = 2 is an eigenvalue of A. (ii) That same p() is also the characteristic polynomial of AT (iii) A is a 3 x 3 matrix. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True,False,False, then you would enter '1,2,2' into the answer box below (without the quotes).

Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ +62² 15. Consider the following statements. (1) λ = 2 is an eigenvalue of A. (ii) That same p() is also the characteristic polynomial of AT (iii) A is a 3 x 3 matrix. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True,False,False, then you would enter '1,2,2' into the answer box below (without the quotes).

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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Please show step-by-step solution and do not skip steps. Explain your entire process in great detail. Explain how you reached the answer you did.

 

Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ + 62² - 15. Consider the following statements. (1) λ = 2 is an eigenvalue of A. (11) That same p(2) is also the characteristic polynomial of A¹. (111) A is a 3 x 3 matrix. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False,False, then you would enter '1.2.2' into the answer box below (without the quotes).
Transcribed Image Text:Problem #4: Suppose that a matrix A has characteristic polynomial p() = 24 - 32³ + 62² - 15. Consider the following statements. (1) λ = 2 is an eigenvalue of A. (11) That same p(2) is also the characteristic polynomial of A¹. (111) A is a 3 x 3 matrix. Determine which of the above statements are True (1) or False (2). So, for example, if you think that the answers, in the above order, are True False,False, then you would enter '1.2.2' into the answer box below (without the quotes).
Expert Solution
Step 1: We will check 2 is an eigenvalue of the matrix A.

(i). Given characteristic polynomial is p(λ)=λ4−3λ3+6λ2−15.

If λ=2 is an eigenvalue of A then p(2)=0.

Now, p(2)=24−3(2)3+6(2)2−15p(2)=16−24+24−15p(2)=1≠0

Hence, λ=2 is not an eigenvalue of A.

The first statement is false.

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