Question
Download Solution PDFThe eigen values of A =
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Step 1: Characteristic matrix [ A - λI]
Step 2: To find eigen-value of the matrix, find the determinant of |A - λI| = 0
Calculation:
Given:
Step 1: Characteristic matrix [ A - λI]
Step 2: To find eigen value of the matrix, find the determinant of |A - λI| = 0
⇒ (2 -λ)[(λ - 2) (1 + λ) -4] -2[4 - 2λ - 8] + [4 + 4(1 + λ)] = 0
⇒ (2 -λ)[(λ - λ2 - 2 - 2λ -4] -2[- 2λ - 4] + [4 + 4+ 4λ)] = 0
⇒ -λ3 + 3λ2 +24λ + 28 = 0
⇒ (λ +2) (-λ2 + 5λ + 14) = 0
⇒ (λ +2) (λ2 - 5λ - 14) = 0
∴ λ = -2, -2, 7
Last updated on Apr 14, 2023
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