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If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal to
- a)8
- b)10
- c)9
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal t...
Since the product of the eigenvalues is equal to the determinant of the matrix so |A| = 1 x 2 x 5 = 10
This question is part of UPSC exam. View all Electronics and Communication Engineering (ECE) courses
Most Upvoted Answer
If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal t...
Solution:
Given that the eigenvalues of matrix A are 1, 2 and 5.
Let A be a 3×3 matrix, then the characteristic equation of A is given by
|A-λI|=0 where λ is the eigenvalue of A and I is the identity matrix.
Substituting the given eigenvalues, we get
|A-1I| = 0, |A-2I| = 0 and |A-5I| = 0
Expanding the above expressions, we get
det(A-I) = 0, det(A-2I) = 0 and det(A-5I) = 0
Now, we know that the determinant of a matrix is equal to the product of its eigenvalues.
Hence, det(A) = det(A-I) × det(A-2I) × det(A-5I)
Substituting the values of determinants, we get
|A| = (1-λ)(2-λ)(5-λ)
Putting λ=0 in above expression, we get |A| = 10. Therefore, the correct answer is option 'B'.
Hence, the determinant of matrix A is equal to 10.
Given that the eigenvalues of matrix A are 1, 2 and 5.
Let A be a 3×3 matrix, then the characteristic equation of A is given by
|A-λI|=0 where λ is the eigenvalue of A and I is the identity matrix.
Substituting the given eigenvalues, we get
|A-1I| = 0, |A-2I| = 0 and |A-5I| = 0
Expanding the above expressions, we get
det(A-I) = 0, det(A-2I) = 0 and det(A-5I) = 0
Now, we know that the determinant of a matrix is equal to the product of its eigenvalues.
Hence, det(A) = det(A-I) × det(A-2I) × det(A-5I)
Substituting the values of determinants, we get
|A| = (1-λ)(2-λ)(5-λ)
Putting λ=0 in above expression, we get |A| = 10. Therefore, the correct answer is option 'B'.
Hence, the determinant of matrix A is equal to 10.
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If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1, 2 and 5 are the eigen values of the matrix A then |A| is equal toa)8b)10c)9d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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