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Question Number 13 by user1 last updated on 25/Jan/15
Expand the determnent △= determinant ((a,h,g),(h,b,f),(g,f,c))
Expandthedetermnent△=|ahghbfgfc|
Answered by user1 last updated on 30/Oct/14
Expanding by 1^(st) row, we have: △=a∙ determinant ((b,f),(f,c))−h∙ determinant ((h,f),(g,c))+g∙ determinant ((h,b),(g,f)) =a(bc−f^2 )−h(ch−fg)+g(fh−bg) =(abc+2fgh−af^2 −bg^2 −ch^2 )
Expandingby1strow,wehave:△=a⋅|bffc|−h⋅|hfgc|+g⋅|hbgf|=a(bc−f2)−h(ch−fg)+g(fh−bg)=(abc+2fgh−af2−bg2−ch2)

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