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If A is singular matrix of order n, then a (adj A) equals,
- a)null matrix
- b)row matrix
- c)identity matrix
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If A is singular matrix of order n, then a (adj A) equals,a)null matri...
Explanation:
Definition of Singular Matrix:
- A singular matrix is a square matrix that is not invertible, meaning its determinant is zero.
- If a matrix A is singular, then the product of A and its adjoint (adj A) will result in a null matrix.
Explanation:
- Let A be a singular matrix of order n.
- Since A is singular, det(A) = 0.
- The adjoint of a matrix A is defined as the transpose of the matrix of cofactors of A.
- When A is singular, the determinant of A is zero, which leads to the determinant of adj(A) being zero as well.
- Therefore, a (adj A) will result in a null matrix of order n.
Conclusion:
- So, if A is a singular matrix of order n, then the product a (adj A) will be a null matrix.
This explanation clarifies why the correct answer to the given question is option 'A' - null matrix.
Definition of Singular Matrix:
- A singular matrix is a square matrix that is not invertible, meaning its determinant is zero.
- If a matrix A is singular, then the product of A and its adjoint (adj A) will result in a null matrix.
Explanation:
- Let A be a singular matrix of order n.
- Since A is singular, det(A) = 0.
- The adjoint of a matrix A is defined as the transpose of the matrix of cofactors of A.
- When A is singular, the determinant of A is zero, which leads to the determinant of adj(A) being zero as well.
- Therefore, a (adj A) will result in a null matrix of order n.
Conclusion:
- So, if A is a singular matrix of order n, then the product a (adj A) will be a null matrix.
This explanation clarifies why the correct answer to the given question is option 'A' - null matrix.
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If A is singular matrix of order n, then a (adj A) equals,a)null matrixb)row matrixc)identity matrixd)none of theseCorrect answer is option 'A'. Can you explain this answer?
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If A is singular matrix of order n, then a (adj A) equals,a)null matrixb)row matrixc)identity matrixd)none of theseCorrect answer is option 'A'. 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 A is singular matrix of order n, then a (adj A) equals,a)null matrixb)row matrixc)identity matrixd)none of theseCorrect answer is option 'A'. 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 A is singular matrix of order n, then a (adj A) equals,a)null matrixb)row matrixc)identity matrixd)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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