T6 2 Express the matrix -2 3 12. – ...
Question

# T6 2 Express the matrix -2 3 12. – 27 -1 as the sum of a symmetric and a skew-symmetric matrix, 3

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( int ) (1) Let ( A=left[begin{array}{ccc}6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3end{array}right] ) (note: A isasymmetie We know, symmetic math ( x=frac{1}{2}(A+A) ) [ begin{array}{l} =frac{1}{2}left(left[begin{array}{ccc} 6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3 end{array}right]+left[begin{array}{ccc} 6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3 end{array}right]right) = & frac{1}{2}left[begin{array}{ccc} 12 & -4 & 4 -4 & 6 & -2 4 & -2 & 6 end{array}right] = & {left[begin{array}{ccc} 6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3 end{array}right]} end{array} ] Skew symmeric matoix = ( frac{1}{2}left(A vec{F} A^{prime}right) ) [ =frac{1}{2}left{left[begin{array}{rrr} 6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3 end{array}right]-left[begin{array}{rrr} 6 & -2 & 2 -2 & 3 & -1 2 & -1 & 3 end{array}right]right. ] ( =left[begin{array}{lll}0 & 0 & 0 0 & 0 & 0 0 & 0 & 0end{array}right] )