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Which of the below-given statements is/are true?
I. The eigenvalue of the lower triangular matrix is just the diagonal elements of the matrix.
II. The product of the eigenvalue of a matrix is equal to its trace.
III. If 1/λ is an eigenvalue of A’(inverse of A) then orthogonal of A also have 1/λ as its eigenvalue.
  • a)
    Only I
  • b)
    I and II
  • c)
    I and III
  • d)
    I, II and III
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which of the below-given statements is/are true?I. The eigenvalue of t...
  • The eigenvalue of the triangular (lower or upper) matrix are just the diagonal elements of matrix.
  • The product of the eigenvalue of a matrix is equal to its determinants.
  • If λ is the eigenvalue of matrix, then 1/λ is the eigenvalue of its inverse since orthogonal is equal to inverse matrix then it has 1/λ as its eigenvalue

​Example:
Eigenvalues are 1, 4 and 6 (diagonal elements)
Product of eigen value = determinants = 1 × 4 × 6 = 24
Orthogonal matrix and Inverse of given matrix have eigenvalues: 1,1/4 and 1/6
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Which of the below-given statements is/are true?I. The eigenvalue of the lower triangular matrix is just the diagonal elements of the matrix.II. The product of the eigenvalue of a matrix is equal to its trace.III. If1/λ is an eigenvalue of A’(inverse of A) then orthogonal of A also have1/λ as its eigenvalue.a)Only Ib)I and IIc)I and IIId)I, II and IIICorrect answer is option 'C'. Can you explain this answer?
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Which of the below-given statements is/are true?I. The eigenvalue of the lower triangular matrix is just the diagonal elements of the matrix.II. The product of the eigenvalue of a matrix is equal to its trace.III. If1/λ is an eigenvalue of A’(inverse of A) then orthogonal of A also have1/λ as its eigenvalue.a)Only Ib)I and IIc)I and IIId)I, II and IIICorrect answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Which of the below-given statements is/are true?I. The eigenvalue of the lower triangular matrix is just the diagonal elements of the matrix.II. The product of the eigenvalue of a matrix is equal to its trace.III. If1/λ is an eigenvalue of A’(inverse of A) then orthogonal of A also have1/λ as its eigenvalue.a)Only Ib)I and IIc)I and IIId)I, II and IIICorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the below-given statements is/are true?I. The eigenvalue of the lower triangular matrix is just the diagonal elements of the matrix.II. The product of the eigenvalue of a matrix is equal to its trace.III. If1/λ is an eigenvalue of A’(inverse of A) then orthogonal of A also have1/λ as its eigenvalue.a)Only Ib)I and IIc)I and IIId)I, II and IIICorrect answer is option 'C'. Can you explain this answer?.
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