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Matrix questions help

發問:

1 a)Prove that if A is an n x n matrix, then B = A+A’ is symmetric b) Prove that if A and B are n x n symmetric matrices, then AB is symmetric if and only if AB = BA Can someone pls help. Thanks~

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• 無印良品筆+hi-tec-c coleto~@1@
• 大埔區小學校際田徑錦標賽-英文(20點)@1@
• 中二數學-因式分解

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1 a)Prove that if A is an n x n matrix, then B = A+A’ is symmetric The (i,j) element of B is bij=aij+aji The (i,j) element of B' is b'ij=bji=aji+aij So bij=b'ij B = A+A’ is symmetric (b) if AB is symmetric AB=(AB)' So AB=B'A'=BA (A and B are n x n symmetric matrices) Conversly if AB=BA AB=B'A' (A and B are n x n symmetric matrices) AB=(AB)' Shows that AB is symmetric

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