Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Find the Eigen values of matrix:a)b)2, 1, 2c)...
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Find the Eigen values of matrix:
- a)
- b)2, 1, 2
- c)2, 2, 0
- d)2, 2, 2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Find the Eigen values of matrix:a)b)2, 1, 2c)2, 2, 0d)2, 2, 2Correct a...
To find the Eigen values it satisfy the condition,
|A − λI| = 0
= (2 − λ)((2 − λ)2 − 1) − 1((2 − λ) − 0) + 0
= (2 − λ)(4 + λ2 − 4λ − 1) − 2 + λ
= (2 − λ)(λ2 − 4λ + 3) − 2 + λ
= (-λ3 + 6λ2 − 11λ + 6) − 2 + λ
= −λ3 + 6λ2 − 10λ + 4
= −λ3 + 2λ2 + 4λ2 − 8λ − 2λ + 4
= −λ2(λ − 2) + 4λ(λ − 2) − 2(λ − 2)
= (λ − 2)(−λ2 + 4λ − 2)… (i)
By using Shri Dronacharya's formula for quadratic equation, we get,
So,
And from equation (i) we get,
⇒ x = 2
By solving the above equation, we get,
Hence, the correct option is (A).
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