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prawinath
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Homework Statement
aij is a symmetric matrix
bij is a an anti symmetric matrix
prove that aij * bij = 0
Homework Equations
aij * bij
The Attempt at a Solution
any one got any ideas ?
A symmetric matrix is a square matrix where the elements are equal to their corresponding elements reflected across the main diagonal. In other words, the element in the i-th row and j-th column is equal to the element in the j-th row and i-th column.
A matrix can be proven to be symmetric by checking if it is equal to its own transpose. If the matrix A is equal to its transpose AT, then it is symmetric.
A matrix is anti symmetric if it is equal to the negative of its own transpose. This means that the element in the i-th row and j-th column is equal to the negative of the element in the j-th row and i-th column.
To show that a matrix is anti symmetric, you need to check if it is equal to the negative of its own transpose. If the matrix A is equal to -AT, then it is anti symmetric.
No, a matrix cannot be both symmetric and anti symmetric. This is because if a matrix is symmetric, it means that it is equal to its own transpose, while if it is anti symmetric, it is equal to the negative of its own transpose. These two conditions cannot be satisfied simultaneously.