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Which of the following statements is/are incorrect?
(i) Adjoint of a symmetric matrix is symmetric.
(ii) Adjoint of a unit matrix is a unit matrix.
(iii) A (adj a) = (adj A) A = |A|
(iv) Adjoint of a diagonal matrix is a diagonal matrix.
(ii) Adjoint of a unit matrix is a unit matrix.
(iii) A (adj a) = (adj A) A = |A|
(iv) Adjoint of a diagonal matrix is a diagonal matrix.
- a)(i)
- b)(ii)
- c)(iii) and (iv)
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Which of the following statements is/are incorrect?(i) Adjoint of a sy...
d) None of these All of the statements are correct.
(i) Adjoint of a symmetric matrix is symmetric. This is true because the adjoint of any matrix is the transpose of its conjugate,and if the matrix is symmetric, its transpose is the same as its conjugate.
(ii) Adjoint of a unit matrix is a unit matrix.This is true because the adjoint of a unit matrix is simply its transpose, which is also a unit matrix.
(iii) A(adja) (adjA)A=|A|.This is true because the adjoint of any matrix is the transpose of its conjugate,so A(adja)=(adjA) A= the transpose of the conjugate of A times A,which is equal to the determinant of A.
(iv) Adjoint of a diagonal matrix is adiagonal matrix. This is also true because the adjoint of a diagonal matrix is simply its transpose, which is also diagonal.
(i) Adjoint of a symmetric matrix is symmetric. This is true because the adjoint of any matrix is the transpose of its conjugate,and if the matrix is symmetric, its transpose is the same as its conjugate.
(ii) Adjoint of a unit matrix is a unit matrix.This is true because the adjoint of a unit matrix is simply its transpose, which is also a unit matrix.
(iii) A(adja) (adjA)A=|A|.This is true because the adjoint of any matrix is the transpose of its conjugate,so A(adja)=(adjA) A= the transpose of the conjugate of A times A,which is equal to the determinant of A.
(iv) Adjoint of a diagonal matrix is adiagonal matrix. This is also true because the adjoint of a diagonal matrix is simply its transpose, which is also diagonal.
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Which of the following statements is/are incorrect?(i) Adjoint of a sy...
Incorrect Statements about Adjoint Matrix
Statement: Adjoint of a symmetric matrix is symmetric.
Incorrect
Explanation: The adjoint matrix, also known as the adjugate or classical adjoint, of a matrix A is the transpose of its cofactor matrix. The adjoint of a symmetric matrix may or may not be symmetric.
Statement: Adjoint of a unit matrix is a unit matrix.
Incorrect
Explanation: The adjoint of a unit matrix is not necessarily a unit matrix. The adjoint of a matrix A is defined as the transpose of its cofactor matrix, which depends on the elements of A.
Statement: A (adj A) = (adj A) A = |A|
Incorrect
Explanation: The correct statement is A(adj A) = (adj A)A = |A|I, where I is the identity matrix.
Statement: Adjoint of a diagonal matrix is a diagonal matrix.
Incorrect
Explanation: The adjoint of a diagonal matrix is not necessarily a diagonal matrix. The adjoint matrix is obtained by taking the transpose of the cofactor matrix of the original matrix, which may not preserve the diagonal structure of the matrix.
Statement: Adjoint of a symmetric matrix is symmetric.
Incorrect
Explanation: The adjoint matrix, also known as the adjugate or classical adjoint, of a matrix A is the transpose of its cofactor matrix. The adjoint of a symmetric matrix may or may not be symmetric.
Statement: Adjoint of a unit matrix is a unit matrix.
Incorrect
Explanation: The adjoint of a unit matrix is not necessarily a unit matrix. The adjoint of a matrix A is defined as the transpose of its cofactor matrix, which depends on the elements of A.
Statement: A (adj A) = (adj A) A = |A|
Incorrect
Explanation: The correct statement is A(adj A) = (adj A)A = |A|I, where I is the identity matrix.
Statement: Adjoint of a diagonal matrix is a diagonal matrix.
Incorrect
Explanation: The adjoint of a diagonal matrix is not necessarily a diagonal matrix. The adjoint matrix is obtained by taking the transpose of the cofactor matrix of the original matrix, which may not preserve the diagonal structure of the matrix.
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Which of the following statements is/are incorrect?(i) Adjoint of a sy...
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Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is/are incorrect?(i) Adjoint of a symmetric matrix is symmetric. (ii) Adjoint of a unit matrix is a unit matrix.(iii) A (adj a) = (adj A) A = |A| (iv) Adjoint of a diagonal matrix is a diagonal matrix.a)(i)b)(ii)c)(iii) and (iv)d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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