Answer & Explanation
as we know that a matrix E is said to be symmetric if and skew symmetric if
as therefore, B is symmetric matrix.
as therefore, C is skew symmetric matrix. Hence proved.
Now we have to show that every nxxn matrix can be expressed as the sum of the symmetric and skew symmetric matrix. Let A be nxxn matrix. therefore,
where and B is a symmetric matrix and and C is a skew symmetric matrix.
(symmetric matrix +skew symmetric matrix)
therefore, it has been showed that any matrix A of order nxxn can be expressed as the sum of symmetric and skew symmetric matrix.
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