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Express the matrix A={:[(2,-3,4),(-1,4,3...

Express the matrix `A={:[(2,-3,4),(-1,4,3),(1,-2,3)]:}` as the sum of a symmetric and a skew symmetric matrix

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Given `A={:[(2,-3,4),(-1,4,3),(1,-2,3)]:}`
`A'={:[(2,-1,1),(-3,4,-2),(4,3,3)]:}`
Let `P=*(1)/(2)(A+A')=(1)/(2){{:[(2,03,4),(-1,4,3),(1,-2,3)]:}+[(2,-1,1),(-3,4,-2),(4,3,3)]:}}`
`=(1)/(2){:[(4,-4,5),(-4,8,1),(5,1,6)]:}={:[(2,-1,(5)/(2)),(-2,4,(1)/(2)),((5)/(2),(1)/(2),3)]:}" (Symmetric matrix)"`
`Q=(1)/(2)(A-A')=(1)/(2){:{[(2,-3,4),(-1,8,1),(5,1,6)]:}={:[(2,-1,1),(-3,4,-2),(4,3,3)]:}}`
`=(1)/(2){{:[(0,-2,3),(2,0,5),(-2,-5,0)]:}}`
`={:[(0,-1,(3)/(2)),(1,0,(5)/(2)),(-(3)/(2),-(5)/(2),0)]:}" (Skew symmetric matrix)"`
Now, A=P+Q
`={:[(2,-2,(5)/(2)),(-2,4,(1)/(2)),((5)/(2),(1)/(2),3)]:}+{:[(0,-1,(3)/(2)),(1,0,(5)/(2)),(-(3)/(2),-(5)/(2),0)]:}`
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