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Addition of Matrices

Addition of Matrices

If [A] and [B] are two matrices of same order, [A] + [B] is defined as matrix formed by sum of corresponding elements.

Addition
GATE matrix algebra
GATE matrix algebra
GATE matrix algebra

Square Matrix as a Sum of Symmetric and Skew-Symmetric Matrix:

Symm+skew symm
GATE matrix algebra

where,

GATE matrix algebra

(M + Trnas. of M) is a Symmetric matrix.

GATE matrix algebra

(M - Trnas. of M) is a Skew-Symmetric matrix.

In this way, any square matrix may be written as the sum of its symmetric and skew-symmetric parts.

Example:

GATE 2020: A matrix P is decomposed into its Symmetric part S and Skew-Symmetric part V. Find the matrix P.

Exmaples
GATE 2020 solved
GATE 2020 solved
GATE 2020 solved
GATE 2020 solved
GATE 2020 solved
GATE 2020 solved

Solution:

Matrix M = Symmetric part + Skew-Symmetric part

M = S + V

Adding S & V, M comes out to be

GATE 2020 solved

So, B is the correct answer.

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