Let A be an nxn matrix with real entries, and let λ be an eigenvalue of. Which of the following statements iscorrect? (i) aλ is an eigenvalue of aA for all real scalars a (ii) 2² is an eigenvalue of A² (ii) 2²+ aλ +ß is an eigenvalue of A²+A+BI for all real scalars a and B; (iv) If λ = a +ib with a,b #0 are some real numbers then = a-ib is also an eiegenvalue of A. O A. only (1) O B. only (ii) OC. only (iv) O D. only (iii) O E. (i), (ii), (iii), (iv) OF. only (ii) and (iv)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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QUESTION 9
Let A be an nxn matrix with real entries, and let A be an eigenvalue of A. Which of the following
statements iscorrect?
(i) al is an eigenvalue of aA for all real scalars a
(ii) 2² is an eigenvalue of A?
(ii) 2² + a2 +B is an eigenvalue of A? + aA+ ßI for all real scalars a and ß;
(iv) If A = a+ib with a,b +0 are some real numbers then 7 = a – ib is also an eiegenvalue of A.
O A. only (i)
B. only (ii)
O C. only (iv)
D. only (ii)
O E. (i), (ii), (ii), (v)
O F. only (ii) and (iv)
Transcribed Image Text:QUESTION 9 Let A be an nxn matrix with real entries, and let A be an eigenvalue of A. Which of the following statements iscorrect? (i) al is an eigenvalue of aA for all real scalars a (ii) 2² is an eigenvalue of A? (ii) 2² + a2 +B is an eigenvalue of A? + aA+ ßI for all real scalars a and ß; (iv) If A = a+ib with a,b +0 are some real numbers then 7 = a – ib is also an eiegenvalue of A. O A. only (i) B. only (ii) O C. only (iv) D. only (ii) O E. (i), (ii), (ii), (v) O F. only (ii) and (iv)
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