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8. For each of the following, find all possible values of the scalar a that make the matrix defective or show that no such values exist. (a) (c) (e) (g) (h) 1 1 2 2 1 1 0 1 1 0 0 0 α 1 1 | a α +2 0 0 3α 1 0 0 0 a+2 0 2 0 1 0 α −1 α 0 0 0 α 1 a +2 0 0 a +2 0 0 2a 0 1 2α 1 1 (b) 1 1 0 0 (d) (f) 1 4 -1 [₁ 0 За 0 0 1 1 α 6 −1 0 0 0 α 1 0 α -2 1 α

8. For each of the following, find all possible values of the scalar a that make the matrix defective or show that no such values exist. (a) (c) (e) (g) (h) 1 1 2 2 1 1 0 1 1 0 0 0 α 1 1 | a α +2 0 0 3α 1 0 0 0 a+2 0 2 0 1 0 α −1 α 0 0 0 α 1 a +2 0 0 a +2 0 0 2a 0 1 2α 1 1 (b) 1 1 0 0 (d) (f) 1 4 -1 [₁ 0 За 0 0 1 1 α 6 −1 0 0 0 α 1 0 α -2 1 α

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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only g and h

8. For each of the following, find all possible values of the scalar a that make the matrix defective or show that no such values exist. (a) (c) (e) (g) (h) 1 1 2 2 1 1 0 1 1 0 0 0 α 1 1 | a 3α 1 0 α +2 0 0 0 2 0 1 0 α a+2 0 0 −1 α 0 0 0 α 1 a +2 0 0 2a 0 0 a +2 1 0 2α 1 1 (b) 1 1 0 0 (d) (f) 1 4 -1 [₁ 0 За 0 0 1 1 α 6 −1 0 0 0 α 1 0 α -2 1 α
Transcribed Image Text:8. For each of the following, find all possible values of the scalar a that make the matrix defective or show that no such values exist. (a) (c) (e) (g) (h) 1 1 2 2 1 1 0 1 1 0 0 0 α 1 1 | a 3α 1 0 α +2 0 0 0 2 0 1 0 α a+2 0 0 −1 α 0 0 0 α 1 a +2 0 0 2a 0 0 a +2 1 0 2α 1 1 (b) 1 1 0 0 (d) (f) 1 4 -1 [₁ 0 За 0 0 1 1 α 6 −1 0 0 0 α 1 0 α -2 1 α
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