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anonymous
 5 years ago
B is a square matrix., and A = B+B^T. Prove that every such A is symmetric.
anonymous
 5 years ago
B is a square matrix., and A = B+B^T. Prove that every such A is symmetric.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0must be symmetric. If B has entries (bij) and B^T has entries (cij) then since it is the transpose, cij = bji. Therefore in the sum A = B+B^T each aij = bij + cij = bij +bji. Symmetric means aij = aji: aij = bij + bji = bji + bij = aji.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hope this is clear. if not let me know.
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