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Is it possible to tell Mathematica to transform algebraic expressions into matrices/determinants etc?
In its simplest form what I'm looking for is:
In:= FullestSimplify[-b c + a d]
(* Out:=Det[{{a, c}, {b, d}}] *)
Another example:
In:= FullestSimplify[a - b + c - b c - d + a d]
(* Out:= .....