For any matrix A, what is (A + A^T) called if A is a square matrix?a.Diagonal matrixb.Symmetric matrixc.Skew-symmetric matrixd.Identity matrix
Question
For any matrix A, what is (A + A^T) called if A is a square matrix?a.Diagonal matrixb.Symmetric matrixc.Skew-symmetric matrixd.Identity matrix
Solution
The matrix (A + A^T) is called a Symmetric matrix.
Here's why:
A symmetric matrix is defined as a matrix that is equal to its transpose. If A is any given matrix, A^T denotes the transpose of matrix A.
The transpose of a matrix is achieved by flipping it over its diagonal, swapping the row and column indices of each element.
So, if we add matrix A and its transpose A^T, we get a symmetric matrix because the definition of a symmetric matrix is one where A is equal to its transpose, A^T.
Therefore, the answer is b. Symmetric matrix.
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