Lösung Gemischte Aufgaben

Zuletzt geändert von akukin am 2024/02/07 18:18

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

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

c) 6\left(\begin{array}{c}-1\\6 \end{array}\right)=\left(\begin{array}{c}6 \cdot (-1)\\6 \cdot 6 \end{array}\right)=\left(\begin{array}{c}-6\\36 \end{array}\right)

d) \frac{1}{3}\left(\begin{array}{c}-3\\18 \end{array}\right)=\left(\begin{array}{c} \frac{1}{3} \cdot (-3) \\ \frac{1}{3} \cdot 18 \end{array}\right)=\left(\begin{array}{c} -1 \\ 6 \end{array}\right)

e) 2\left(\begin{array}{c}\frac{3}{7}\\5 \end{array}\right)+ 3\left(\begin{array}{c}\frac{5}{7}\\5 \end{array}\right)-4\left(\begin{array}{c}\frac{1}{7}\\5 \end{array}\right)= \left(\begin{array}{c} 2\cdot \frac{3}{7} + 3 \cdot \frac{5}{7} - 4 \cdot \frac{1}{7} \\ 2 \cdot 5 + 3 \cdot 5 - 4\cdot 5 \end{array}\right)= \left(\begin{array}{c} \frac{6}{7} + \frac{15}{7} - \frac{4}{7} \\ 10 + 15 - 20 \end{array}\right)= \left(\begin{array}{c} \frac{17}{7} \\ 5 \end{array}\right)

f)-2\left(\begin{array}{c}1\\0,5\\4\end{array}\right)-4\left(\begin{array}{c}-1\\0,5\\4\end{array}\right)+\frac{1}{2}\left(\begin{array}{c}-1\\-2\\20\end{array}\right)= \left(\begin{array}{c}(-2)\cdot 1-4 \cdot (-1)+ \frac{1}{2} \cdot (-1)\\(-2)\cdot 0,5- 4 \cdot 0,5+ \frac{1}{2}\cdot (-2)\\(-2) \cdot 4 - 4 \cdot 4 + \frac{1}{2} \cdot 20\end{array}\right)= \left(\begin{array}{c}-2+4-\frac{1}{2} \\-1- 2-1\\-8 - 16+ 10\end{array}\right)= \left(\begin{array}{c}\frac{3}{2} \\-4\\-14\end{array}\right)