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Addition of Matrices
Addition of Matrices
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If [A] and [B] are two matrices of same order, [A] + [B] is defined as matrix formed by sum of corresponding elements.
Addition
Square Matrix as a Sum of Symmetric and Skew-Symmetric Matrix:
Symm+skew symm
where,
(M + Trnas. of M) is a Symmetric matrix.
(M - Trnas. of M) is a Skew-Symmetric matrix.
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In this way, any square matrix may be written as the sum of its symmetric and skew-symmetric parts.
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Example:
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GATE 2020: A matrix P is decomposed into its Symmetric part S and Skew-Symmetric part V. Find the matrix P.
Exmaples
Solution:
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Matrix M = Symmetric part + Skew-Symmetric part
M = S + V
Adding S & V, M comes out to be
So, B is the correct answer.
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