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If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A are
- a)3/4, -(1/2)
- b)4/3, -2
- c)12, -8
- d)-12, -8
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4,...
Given Information:
- Eigen values of matrix A: 3, -2
- Determinant of matrix A: |A| = 4
Explanation:
Finding the Eigen values of Adj A:
- The determinant of the adjoint of a matrix is equal to the determinant of the original matrix raised to the power of (n-1), where n is the order of the matrix.
- In this case, the determinant of adj A = |A|^(n-1) = 4^(2-1) = 4
- Therefore, the product of the eigen values of adj A is 4.
Calculating the Eigen values of Adj A:
- Let the eigen values of adj A be x and y.
- Since the product of the eigen values of adj A is 4, we have x * y = 4.
- Given that the eigen values of adj A are in the form of (x, y) = (4/3, -2) or (-4/3, 2)
Conclusion:
- The correct option is b) 4/3, -2 as the eigen values of adj A are in the form of (4/3, -2).
- Eigen values of matrix A: 3, -2
- Determinant of matrix A: |A| = 4
Explanation:
Finding the Eigen values of Adj A:
- The determinant of the adjoint of a matrix is equal to the determinant of the original matrix raised to the power of (n-1), where n is the order of the matrix.
- In this case, the determinant of adj A = |A|^(n-1) = 4^(2-1) = 4
- Therefore, the product of the eigen values of adj A is 4.
Calculating the Eigen values of Adj A:
- Let the eigen values of adj A be x and y.
- Since the product of the eigen values of adj A is 4, we have x * y = 4.
- Given that the eigen values of adj A are in the form of (x, y) = (4/3, -2) or (-4/3, 2)
Conclusion:
- The correct option is b) 4/3, -2 as the eigen values of adj A are in the form of (4/3, -2).
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If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer?
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If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer?.
If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3, -2, are the eigen values of a non-singular matrix A and |A| = 4, then the eigen values of adj A area)3/4, -(1/2)b)4/3, -2c)12, -8d)-12, -8Correct answer is option 'B'. Can you explain this answer?.
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