Matrixprodukt/2x2/C/2/Aufgabe/Lösung

Es ist

${}{\begin{aligned}{\begin{pmatrix}1-{\mathrm {i} }&3-{\mathrm {i} }\\2&1+{\mathrm {i} }\end{pmatrix}}{\begin{pmatrix}1+{\mathrm {i} }&2-{\mathrm {i} }\\2+3{\mathrm {i} }&3-{\mathrm {i} }\end{pmatrix}}&={\begin{pmatrix}{\left(1-{\mathrm {i} }\right)}{\left(1+{\mathrm {i} }\right)}+{\left(3-{\mathrm {i} }\right)}{\left(2+3{\mathrm {i} }\right)}&{\left(1-{\mathrm {i} }\right)}{\left(2-{\mathrm {i} }\right)}+{\left(3-{\mathrm {i} }\right)}{\left(3-{\mathrm {i} }\right)}\\2{\left(1+{\mathrm {i} }\right)}+{\left(1+{\mathrm {i} }\right)}{\left(2+3{\mathrm {i} }\right)}&2{\left(2-{\mathrm {i} }\right)}+{\left(1+{\mathrm {i} }\right)}{\left(3-{\mathrm {i} }\right)}\end{pmatrix}}\\&={\begin{pmatrix}2+9+7{\mathrm {i} }&1-3{\mathrm {i} }+8-6{\mathrm {i} }\\2+2{\mathrm {i} }-1+5{\mathrm {i} }&4-2{\mathrm {i} }+4+2{\mathrm {i} }\end{pmatrix}}\\&={\begin{pmatrix}11+7{\mathrm {i} }&9-9{\mathrm {i} }\\1+7{\mathrm {i} }&8\end{pmatrix}}.\end{aligned}}$

Zur gelösten Aufgabe