Lösung: Rechnen mit Vektoren
Hausaufgabe
Berechnen Sie.
\(2 \cdot \left(\begin{array}{c} 1 \\ 2 \\ -1 \end{array}\right) -3 \cdot \left(\begin{array}{c} 0 \\ 1 \\ -1 \end{array}\right) +\dfrac{1}{2} \cdot \left(\begin{array}{c} 2 \\ -2 \\ 4 \end{array}\right) \)
\( = \left(\begin{array}{c} 2 \cdot 1 \\ 2 \cdot 2 \\ 2 \cdot (-1) \end{array}\right) - \left(\begin{array}{c} 3 \cdot 0 \\ 3 \cdot 1 \\ 3 \cdot (-1) \end{array}\right) + \left(\begin{array}{c} \dfrac{1}{2} \cdot 2 \\ \dfrac{1}{2} \cdot (-2) \\ \dfrac{1}{2} \cdot 4 \end{array}\right) \)
\( = \left(\begin{array}{c} 2 \\ 4 \\ -2 \end{array}\right) - \left(\begin{array}{c} 0 \\ 3 \\ -3 \end{array}\right) + \left(\begin{array}{c} 1 \\ -1 \\ 2 \end{array}\right) \)
\( = \left(\begin{array}{c} 3 \\ 0 \\ 3 \end{array}\right) \)