Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Find eigen values of.a)0, 2, 4b)0, 0, 6c)2, 4...
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Find eigen values of
.
.- a)0, 2, 4
- b)0, 0, 6
- c)2, 4, 9
- d)1, 2, 3
Correct answer is option 'D'. Can you explain this answer?
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Find eigen values of.a)0, 2, 4b)0, 0, 6c)2, 4, 9d)1, 2, 3Correct answe...
⇒ (1 – λ) [(2 – λ) (3 – λ) – 2] – 0 [1(3 – λ) – 2] – 1[2 – 2(2 – λ)] = 0
⇒ (1 – λ) (6 – 2λ – 3λ + λ2 – 2) – 0 – 1(2 – 4 + 2λ) = 0
⇒ (1 – λ) (λ2 – 5λ + 4) – 1(–2 + 2λ) = 0
(1 – λ) (λ2 – 5λ + 4) + 2 – 2λ = 0
(1 – λ) (λ2 – 5λ + 4) + 2(1 – λ) = 0
(1 – λ) (λ2 – 5λ + 4 + 2) = 0
(1 – λ) = 0
λ = 1
λ2 – 5λ + 6 = 0
λ2 – 3λ – 2λ + 6 = 0
λ(λ – 2) (λ – 3) = 0
(λ – 2) (λ – 3) = 0
λ = 2,λ = 3
Eigen values are 1, 2, 3.
⇒ (1 – λ) (6 – 2λ – 3λ + λ2 – 2) – 0 – 1(2 – 4 + 2λ) = 0
⇒ (1 – λ) (λ2 – 5λ + 4) – 1(–2 + 2λ) = 0
(1 – λ) (λ2 – 5λ + 4) + 2 – 2λ = 0
(1 – λ) (λ2 – 5λ + 4) + 2(1 – λ) = 0
(1 – λ) (λ2 – 5λ + 4 + 2) = 0
(1 – λ) = 0
λ = 1
λ2 – 5λ + 6 = 0
λ2 – 3λ – 2λ + 6 = 0
λ(λ – 2) (λ – 3) = 0
(λ – 2) (λ – 3) = 0
λ = 2,λ = 3
Eigen values are 1, 2, 3.
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