Beispiel: Vielfaches eines Vektors (Skalarmultiplikation)

Berechnen Sie.

\(3 \cdot \left(\begin{array}{c} -1 \\ 2 \\ 1 \end{array}\right) \)

\(3 \cdot \left(\begin{array}{c} -1 \\ 2 \\ 1 \end{array}\right) = \left(\begin{array}{c} 3 \cdot (-1) \\ 3 \cdot 2 \\ 3 \cdot 1 \end{array}\right) = \left(\begin{array}{c} -3 \\ 6 \\ 3 \end{array}\right) \)

Berechnen Sie.

\( \dfrac{1}{2} \cdot \left(\begin{array}{c} -4 \\ 2 \\ 6 \end{array}\right) \)

\( \dfrac{1}{2} \cdot \left(\begin{array}{c} -4 \\ 2 \\ 6 \end{array}\right) = \left(\begin{array}{c} \dfrac{1}{2} \cdot (-4) \\ \dfrac{1}{2} \cdot 2 \\ \dfrac{1}{2} \cdot 6 \end{array}\right) = \left(\begin{array}{c} -2 \\ 1 \\ 3 \end{array}\right) \)