Determinante/C/Berechne/3x3/2/Aufgabe/Lösung

Es ist

{}{\begin{aligned}&\,\,\,\,\,\,\,\det {\begin{pmatrix}-2-{\mathrm {i} }&3-4{\mathrm {i} }&2{\mathrm {i} }\\0&6+7{\mathrm {i} }&4\\3+3{\mathrm {i} }&4-3{\mathrm {i} }&-4-{\mathrm {i} }\end{pmatrix}}\\&={\left(-2-{\mathrm {i} }\right)}\cdot \det {\begin{pmatrix}6+7{\mathrm {i} }&4\\4-3{\mathrm {i} }&-4-{\mathrm {i} }\end{pmatrix}}+{\left(3+3{\mathrm {i} }\right)}\cdot \det {\begin{pmatrix}3-4{\mathrm {i} }&2{\mathrm {i} }\\6-7{\mathrm {i} }&4\end{pmatrix}}\\&={\left(-2-{\mathrm {i} }\right)}\cdot {\left({\left(6+7{\mathrm {i} }\right)}{\left(-4-{\mathrm {i} }\right)}-4{\left(4-3{\mathrm {i} }\right)}\right)}+{\left(3+3{\mathrm {i} }\right)}\cdot {\left(4{\left(3-4{\mathrm {i} }\right)}-2{\mathrm {i} }{\left(6-7{\mathrm {i} }\right)}\right)}\\&={\left(-2-{\mathrm {i} }\right)}\cdot {\left(-47-22{\mathrm {i} }\right)}+{\left(3+3{\mathrm {i} }\right)}\cdot {\left(-2-28{\mathrm {i} }\right)}\\&=72+91{\mathrm {i} }+78-82{\mathrm {i} }\\&=150+9{\mathrm {i} }.\,\end{aligned}}

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