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If A is a singular matrix then Adj A is
- a)non-singular
- b)singular
- c)symmetric
- d)skew-symmetric
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If A is a singular matrix then Adj A isa)non-singularb)singularc)symme...
Explanation:
A singular matrix is a matrix that does not have an inverse. This means that if we try to find the inverse of a singular matrix, we will not be able to do so. The determinant of a singular matrix is zero.
The adjugate matrix, or adjoint matrix, of a matrix A is the transpose of the matrix of cofactors of A. The cofactor of an element in a matrix is the determinant of the matrix obtained by deleting the row and column that contain that element, multiplied by (-1)^(i+j), where i and j are the row and column indices of the element.
If A is a singular matrix, then its determinant is zero. This means that at least one of the cofactors of A is zero. Therefore, at least one element of the adjugate matrix of A is zero. This means that the adjugate matrix of A is not invertible, or non-singular.
Therefore, the correct answer is (b) singular.
A singular matrix is a matrix that does not have an inverse. This means that if we try to find the inverse of a singular matrix, we will not be able to do so. The determinant of a singular matrix is zero.
The adjugate matrix, or adjoint matrix, of a matrix A is the transpose of the matrix of cofactors of A. The cofactor of an element in a matrix is the determinant of the matrix obtained by deleting the row and column that contain that element, multiplied by (-1)^(i+j), where i and j are the row and column indices of the element.
If A is a singular matrix, then its determinant is zero. This means that at least one of the cofactors of A is zero. Therefore, at least one element of the adjugate matrix of A is zero. This means that the adjugate matrix of A is not invertible, or non-singular.
Therefore, the correct answer is (b) singular.
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If A is a singular matrix then Adj A isa)non-singularb)singularc)symmetricd)skew-symmetricCorrect answer is option 'B'. Can you explain this answer?
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