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Can you explain the answer of this question below:
If in a square matrix A=[aij], we find that
aij = aji ∀ i,j, then A is a
aij = aji ∀ i,j, then A is a
- A:symmetric matrix
- B:diagonal matrix
- C:skew symmetric matrix
- D:transpose matrix
- E:undefined
The answer is a.
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Most Upvoted Answer
Can you explain the answer of this question below:If in a square matri...
Explanation:
Symmetric Matrix:
- In a symmetric matrix, the element in the ith row and jth column is equal to the element in the jth row and ith column.
- Mathematically, if a matrix A is symmetric, then aij = aji for all i,j.
- This property ensures that the matrix is symmetric across its main diagonal.
Given Matrix A:
- In the given square matrix A=[aij], we are given that aij = aji for all i,j.
- This means that the matrix A satisfies the condition for a symmetric matrix.
Conclusion:
- Therefore, the given matrix A is a symmetric matrix.
- Option A: Symmetric matrix is the correct answer.
Summary:
- A matrix is symmetric if it is equal to its transpose, i.e., aij = aji for all i,j.
- In the case of the given matrix A, the elements satisfy this condition, making it a symmetric matrix.
Symmetric Matrix:
- In a symmetric matrix, the element in the ith row and jth column is equal to the element in the jth row and ith column.
- Mathematically, if a matrix A is symmetric, then aij = aji for all i,j.
- This property ensures that the matrix is symmetric across its main diagonal.
Given Matrix A:
- In the given square matrix A=[aij], we are given that aij = aji for all i,j.
- This means that the matrix A satisfies the condition for a symmetric matrix.
Conclusion:
- Therefore, the given matrix A is a symmetric matrix.
- Option A: Symmetric matrix is the correct answer.
Summary:
- A matrix is symmetric if it is equal to its transpose, i.e., aij = aji for all i,j.
- In the case of the given matrix A, the elements satisfy this condition, making it a symmetric matrix.
Community Answer
Can you explain the answer of this question below:If in a square matri...
If aij=aji then it is symmetric matrix but if aij=-aji then it is skew symmetric because transpose of A is equal to A for symmetric matrix .and we know that transpose of matrix is defined as aij=aji
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Can you explain the answer of this question below:If in a square matrix A=[aij], we find that aij = aji ∀ i,j, then A is aA:symmetric matrixB:diagonal matrixC:skew symmetric matrixD:transpose matrixE:undefinedThe answer is a.
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Can you explain the answer of this question below:If in a square matrix A=[aij], we find that aij = aji ∀ i,j, then A is aA:symmetric matrixB:diagonal matrixC:skew symmetric matrixD:transpose matrixE:undefinedThe answer is a. for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:If in a square matrix A=[aij], we find that aij = aji ∀ i,j, then A is aA:symmetric matrixB:diagonal matrixC:skew symmetric matrixD:transpose matrixE:undefinedThe answer is a. covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:If in a square matrix A=[aij], we find that aij = aji ∀ i,j, then A is aA:symmetric matrixB:diagonal matrixC:skew symmetric matrixD:transpose matrixE:undefinedThe answer is a..
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