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If A is any square matrix, then A — A* is a
- a)Symmetric matrix
- b)Skew symmetric matrix
- c)Hermitian Matrix
- d)Skew Hermitian Matrix
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If A is any square matrix, then A — A* is aa)Symmetric matrixb)S...
(A − A')' = A' − (A')'
= A' − A
= −(A − A')
Therefore, it is a skew symmetric matrix
Therefore, it is a skew symmetric matrix
Most Upvoted Answer
If A is any square matrix, then A — A* is aa)Symmetric matrixb)S...
(A − A')' = A' − (A')'
= A' − A
= −(A − A')
Therefore, it is a skew symmetric matrix
Therefore, it is a skew symmetric matrix
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Community Answer
If A is any square matrix, then A — A* is aa)Symmetric matrixb)S...
Understanding the Problem
To determine if the expression A - A is a skew-symmetric matrix, let's analyze the components involved.
Definition of Skew-Symmetric Matrix
A matrix B is called skew-symmetric if it satisfies the condition:
- B^T = -B
where B^T is the transpose of matrix B.
Evaluating A - A
1. Expression: A - A equals the zero matrix, which we can denote as O.
2. Transpose: The transpose of O is:
- O^T = O
3. Checking Skew-Symmetry:
- By the definition of skew-symmetric matrices, we check:
O^T = -O
- This holds true, as both sides equal the zero matrix.
Conclusion
Since A - A results in the zero matrix (O), and it satisfies the skew-symmetric condition (O^T = -O), we conclude that:
- The correct answer is indeed option 'D': A - A is a skew-symmetric matrix.
Key Takeaways
- A - A = O: The difference of any matrix with itself is always the zero matrix.
- Zero Matrix Is Skew-Symmetric: The zero matrix meets the criteria for being skew-symmetric.
This analysis confirms that the assertion regarding the nature of A - A is correct.
To determine if the expression A - A is a skew-symmetric matrix, let's analyze the components involved.
Definition of Skew-Symmetric Matrix
A matrix B is called skew-symmetric if it satisfies the condition:
- B^T = -B
where B^T is the transpose of matrix B.
Evaluating A - A
1. Expression: A - A equals the zero matrix, which we can denote as O.
2. Transpose: The transpose of O is:
- O^T = O
3. Checking Skew-Symmetry:
- By the definition of skew-symmetric matrices, we check:
O^T = -O
- This holds true, as both sides equal the zero matrix.
Conclusion
Since A - A results in the zero matrix (O), and it satisfies the skew-symmetric condition (O^T = -O), we conclude that:
- The correct answer is indeed option 'D': A - A is a skew-symmetric matrix.
Key Takeaways
- A - A = O: The difference of any matrix with itself is always the zero matrix.
- Zero Matrix Is Skew-Symmetric: The zero matrix meets the criteria for being skew-symmetric.
This analysis confirms that the assertion regarding the nature of A - A is correct.
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Question Description
If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer?.
If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A is any square matrix, then A — A* is aa)Symmetric matrixb)Skew symmetric matrixc)Hermitian Matrixd)Skew Hermitian MatrixCorrect answer is option 'D'. Can you explain this answer?.
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