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Nullspace Transpose[{{1,1,1,1,1,1,1},{1,1,1,-1,1,-1,-1},{2,-1,2,0,-1,0,0},{3,0,-1,1,0,-1,-1},{3,0,-1,-1,0,1,1},{-8,2,0,0,-2,0,0},{-8,-4,0,0,4,0,0}}]
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