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Given that matrix A = [6 8 5; 4 2 3; 9 7 1] can be expressed as the sum of a symmetric matrix B and a skew-symmetric matrix C, determine B.

1. [6 6 7; 6 2 5; 7 5 1]
2. [0 2 −2; −2 5 −2; 2 2 0]
3. [6 6 7; −6 2 −5; −7 5 1]
4. [0 6 −2; 2 0 −2; −2 −2 0]

Correct answer: [6 6 7; 6 2 5; 7 5 1]

Solution

A + A^T = [[12,12,14],[12,4,10],[14,10,2]], so B = (A+A^T)/2 = [[6,6,7],[6,2,5],[7,5,1]]. (Option 1 shown is the skew-symmetric part, not B.)

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