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13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are eigenvalues of A. (b) A has size 3 × 3, the only eigenvalues of A are 4 and –6, and nullity(A+ 6I3) = 2. (c) A has size 3 x 3, the only eigenvalue of A is –6, and nullity(A+6I3) = 2.

13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are eigenvalues of A. (b) A has size 3 × 3, the only eigenvalues of A are 4 and –6, and nullity(A+ 6I3) = 2. (c) A has size 3 x 3, the only eigenvalue of A is –6, and nullity(A+6I3) = 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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13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are eigenvalues of A. (b) A has size 3 x 3, the only eigenvalues of A are 4 and -6, and nullity(A+ 6I3) = 2. (c) A has size 3 x 3, the only eigenvalue of A is –6, and nullity(A+6I3) = 2. (d) The characteristic polynomial of A is –t(t² – t+6). (e) The characteristic polynomial of A is (1 – t)(t² +2). (f) The characteristic polynomial of A is (4 – t)(2 – t)³ and rank(A – 214) = 3.
Transcribed Image Text:13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are eigenvalues of A. (b) A has size 3 x 3, the only eigenvalues of A are 4 and -6, and nullity(A+ 6I3) = 2. (c) A has size 3 x 3, the only eigenvalue of A is –6, and nullity(A+6I3) = 2. (d) The characteristic polynomial of A is –t(t² – t+6). (e) The characteristic polynomial of A is (1 – t)(t² +2). (f) The characteristic polynomial of A is (4 – t)(2 – t)³ and rank(A – 214) = 3.
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