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If 2 , - 4 are the eigen values of a non–singular matrix A and |A| = 4, then the eigen values of adjA are
- a)1/2 , -1
- b)2 , -1
- c)2 , - 4
- d)8 , -16
Correct 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...
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If 2 , -4 are the eigen values of a non–singular matrix A and |A...
Explanation:
Given that the eigenvalues of a nonsingular matrix A are 2 and -4 and |A| = 4.
We know that the product of eigenvalues of a matrix is equal to the determinant of the matrix, i.e.,
λ1 * λ2 * ... * λn = |A|
Where λ1, λ2, ..., λn are the eigenvalues of A.
Therefore, we can write
2 * (-4) = |A|
-8 = |A|
Since |A| is given to be 4, we can conclude that A^-1 exists, i.e., A is nonsingular.
Now, the eigenvalues of adjA are given by
λ1' = |A|/λ2
λ2' = |A|/λ1
where λ1 and λ2 are the eigenvalues of A.
Substituting the given values, we get
λ1' = 4/-4 = -1
λ2' = 4/2 = 2
Therefore, the eigenvalues of adjA are -1 and 2.
Hence, the correct answer is option B, i.e., 2 and -1.
Given that the eigenvalues of a nonsingular matrix A are 2 and -4 and |A| = 4.
We know that the product of eigenvalues of a matrix is equal to the determinant of the matrix, i.e.,
λ1 * λ2 * ... * λn = |A|
Where λ1, λ2, ..., λn are the eigenvalues of A.
Therefore, we can write
2 * (-4) = |A|
-8 = |A|
Since |A| is given to be 4, we can conclude that A^-1 exists, i.e., A is nonsingular.
Now, the eigenvalues of adjA are given by
λ1' = |A|/λ2
λ2' = |A|/λ1
where λ1 and λ2 are the eigenvalues of A.
Substituting the given values, we get
λ1' = 4/-4 = -1
λ2' = 4/2 = 2
Therefore, the eigenvalues of adjA are -1 and 2.
Hence, the correct answer is option B, i.e., 2 and -1.
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If 2 , -4 are the eigen values of a non–singular matrix A and |A...
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If 2 , -4 are the eigen values of a non–singular matrix A and |A| =4, then the eigen values of adjA area)1/2 , -1b)2 , -1c)2 , - 4d)8 , -16Correct answer is option 'B'. Can you explain this answer?
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