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If 2, - 4 are the eigen values of a non–singular matrix A and |A| = 8, then the eigen values of adjA are:
- a)1/2, -1
- b)2, - 4
- c)2, -1
- d)8, -16
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If 2, -4 are the eigen values of a non–singular matrix A and |A|...
- Eigenvalues of a matrix A are 2 and -4.
- The determinant ∣A∣ = 8.
- For a non-singular matrix A, the eigenvalues of adj(A) are given by λ1n−1 and λ2n−1, where n is the order of the matrix.
- For a 2x2 matrix, the eigenvalues of adj(A) will be 21= 2 and (−4)1= -4.
- Thus, the eigenvalues of adj(A) are 2 and -4.
Correct answer: b) 2, -4.
Most Upvoted Answer
If 2, -4 are the eigen values of a non–singular matrix A and |A|...
Understanding Eigenvalues and the Adjugate Matrix
Eigenvalues are critical in the study of linear transformations represented by matrices. For a given square matrix A, the eigenvalues provide insight into its properties, such as stability and invertibility.
Given Information
- Eigenvalues of matrix A: 2, -4
- Determinant of A: |A| = 8
Eigenvalues of Adj(A)
The adjugate (or adjoint) of a matrix, denoted as adj(A), has eigenvalues related to those of A. The eigenvalues of adj(A) can be derived from the eigenvalues of A using the following key points:
- If λ is an eigenvalue of matrix A, then the corresponding eigenvalue of adj(A) can be expressed as λ^(n-1), where n is the size (dimension) of the matrix A.
- In this case, since A has two eigenvalues (2 and -4), we can compute the eigenvalues of adj(A) based on the assumption that A is a 2x2 matrix (n=2).
Calculating Eigenvalues of Adj(A)
- For λ1 = 2:
Eigenvalue of adj(A) = 2^(2-1) = 2
- For λ2 = -4:
Eigenvalue of adj(A) = (-4)^(2-1) = -4
Conclusion
Thus, the eigenvalues of adj(A) are 2 and -4. This confirms that the correct answer is option 'B': 2, -4. The relationship between the eigenvalues of a matrix and its adjugate highlights the underlying structure of linear transformations, making it essential in various applications within electronics and communication engineering.
Eigenvalues are critical in the study of linear transformations represented by matrices. For a given square matrix A, the eigenvalues provide insight into its properties, such as stability and invertibility.
Given Information
- Eigenvalues of matrix A: 2, -4
- Determinant of A: |A| = 8
Eigenvalues of Adj(A)
The adjugate (or adjoint) of a matrix, denoted as adj(A), has eigenvalues related to those of A. The eigenvalues of adj(A) can be derived from the eigenvalues of A using the following key points:
- If λ is an eigenvalue of matrix A, then the corresponding eigenvalue of adj(A) can be expressed as λ^(n-1), where n is the size (dimension) of the matrix A.
- In this case, since A has two eigenvalues (2 and -4), we can compute the eigenvalues of adj(A) based on the assumption that A is a 2x2 matrix (n=2).
Calculating Eigenvalues of Adj(A)
- For λ1 = 2:
Eigenvalue of adj(A) = 2^(2-1) = 2
- For λ2 = -4:
Eigenvalue of adj(A) = (-4)^(2-1) = -4
Conclusion
Thus, the eigenvalues of adj(A) are 2 and -4. This confirms that the correct answer is option 'B': 2, -4. The relationship between the eigenvalues of a matrix and its adjugate highlights the underlying structure of linear transformations, making it essential in various applications within electronics and communication engineering.
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If 2, -4 are the eigen values of a non–singular matrix A and |A| = 8, then the eigen values of adjA are:a)1/2, -1b)2, - 4c)2, -1d)8, -16Correct answer is option 'B'. Can you explain this answer?
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If 2, -4 are the eigen values of a non–singular matrix A and |A| = 8, then the eigen values of adjA are:a)1/2, -1b)2, - 4c)2, -1d)8, -16Correct answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 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 2, -4 are the eigen values of a non–singular matrix A and |A| = 8, then the eigen values of adjA are:a)1/2, -1b)2, - 4c)2, -1d)8, -16Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 2, -4 are the eigen values of a non–singular matrix A and |A| = 8, then the eigen values of adjA are:a)1/2, -1b)2, - 4c)2, -1d)8, -16Correct answer is option 'B'. Can you explain this answer?.
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