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For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:
- a)det(A) = 7
- b)det(A) = 81
- c)det(A) = 9
- d)det(A) = 4
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
For a skew symmetric even ordered matrix A of integers, which of the f...
A skew symmetric matrix Anxn is a matrix with AT = -A. The matrix of (A) satisfy this condition.
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For a skew symmetric even ordered matrix A of integers, which of the f...
Skew Symmetric Even Ordered Matrix
A skew-symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, A is skew-symmetric if:
A^T = -A
Even-ordered matrix means that the matrix has an even number of rows and columns.
Properties of Skew-Symmetric Matrices
- The diagonal elements of a skew-symmetric matrix are always zero.
- The determinant of a skew-symmetric matrix of odd order is zero.
- The determinant of a skew-symmetric matrix of even order is a perfect square.
Solution
From the given options, we can see that the determinant of matrix A is given by det(A) = 7, 81, 9, and 4.
We know that the determinant of a skew-symmetric matrix of even order is a perfect square. Therefore, options (b), (c), and (d) are possible determinants for matrix A.
However, option (a) is not possible because 7 is not a perfect square. Therefore, the correct answer is option (a).
Conclusion
In conclusion, for a skew-symmetric even ordered matrix A of integers, the determinant must be a perfect square. Therefore, option (a) is not possible.
A skew-symmetric matrix is a square matrix whose transpose is equal to its negative. In other words, A is skew-symmetric if:
A^T = -A
Even-ordered matrix means that the matrix has an even number of rows and columns.
Properties of Skew-Symmetric Matrices
- The diagonal elements of a skew-symmetric matrix are always zero.
- The determinant of a skew-symmetric matrix of odd order is zero.
- The determinant of a skew-symmetric matrix of even order is a perfect square.
Solution
From the given options, we can see that the determinant of matrix A is given by det(A) = 7, 81, 9, and 4.
We know that the determinant of a skew-symmetric matrix of even order is a perfect square. Therefore, options (b), (c), and (d) are possible determinants for matrix A.
However, option (a) is not possible because 7 is not a perfect square. Therefore, the correct answer is option (a).
Conclusion
In conclusion, for a skew-symmetric even ordered matrix A of integers, the determinant must be a perfect square. Therefore, option (a) is not possible.
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For a skew symmetric even ordered matrix A of integers, which of the f...
Option b c and d are perfect square except option a, thus we can say that for skew symmetric Matrix the det. will be perfect square.
Option a is the correct answer as it does not follow this condition.
Option a is the correct answer as it does not follow this condition.
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For a skew symmetric even ordered matrix A of integers, which of the following will not hold true:a)det(A) = 7b)det(A) = 81c)det(A) = 9d)det(A) = 4Correct answer is option 'A'. Can you explain this answer?
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