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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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