Dualraum/Orthogonalraum/Durchschnitt und Summe/Aufgabe

Es sei ${}V$ ein ${}K$ -Vektorraum und ${}U_{1},U_{2}\subseteq V$ seien Untervektorräume. Zeige im Dualraum ${}{V}^{*}$ die Gleichheit

{}{\left(U_{1}\cap U_{2}\right)}^{\perp }=U_{1}^{\perp }+U_{2}^{\perp }\,.

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