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A matrix can be expressed as sum of symmetric and anti-symmetric matrices.

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A matrix can be expressed as sum of symmetric and anti-symmetric matrices.

(a) True

(b) False

The question was posed to me in a job interview.

My enquiry is from Transpose of Matrices in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

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The correct choice is (a) True

Explanation: Since A = (^1⁄2)(A + A^T) + ((^1⁄2)(A – A^T)

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