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Skew Symmetric Matrix

Express the f...

Question

Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

(i)

(ii)

(iii)

(iv)

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Solution

(i)

Thus, is a symmetric matrix.

Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(ii)

Thus, is a symmetric matrix.

Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(iii)

Thus, is a symmetric matrix.

Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q:

(iv)

Thus, is a symmetric matrix.

Thus, is a skew-symmetric matrix.

Representing A as the sum of P and Q:

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Q. Express the following matrices as the sum of a symmetric and a skew symmetric matrix :

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as a sum of symmetric and skew symmetric matrices.

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