Matrix aus Vorlesung

A = {{5, -8, 7, 9}, {2, 0, 4, 6},  {3, 1, 7, 7}, {2, 8, 2, 
          5}}

Det[A]

Entwicklungssatz für Determinanten

Untermatrix[A_, {p_, q_}] := 
      Delete[Transpose[Delete[Transpose[A], q]], p]

    
Clear[Determinante]
Determinante[{{a_}}] := a;
Determinante[
        A_] := 
(∑_(k = 1)^(Length[A]))(((-1))^((1 + k))) A[[k, 1]]*
          Determinante[Untermatrix[A, {k, 1}]]

Untermatrix[A, {2, 3}]

Determinante[A]