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Question

If matrix A=⎡⎢⎣01−14−343−34⎤⎥⎦=B+C, where B is symmetric matrix and C is skew-symmetric matrix.
Then the matrices B and C are:

A
B=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0521523121124⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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B
B=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0521523121124⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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C
C=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0322320722720⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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D
C=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0322320722720⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
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Solution

The correct option is C C=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0322320722720⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥
Here matrix A is expressed as sum of symmetric and skew-symmetric matrix.

Then B=12(A+AT) which is the symmetric part, and C=12(AAT) which is the skew-symmetric part.

Now A=011434334AT=043133144

B=12011434334+043133144=12052561218
B=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0521523121124⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

and C=12011434334043133144=12034307470
C=⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢0322320722720⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

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