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Lösung Vektoraddition rechnerisch

Zuletzt geändert von akukin am 2024/12/22 18:37

a)  
\left(\begin{matrix}12\\7 \end{matrix}\right)+\left(\begin{matrix}2\\4 \end{matrix}\right)=\left(\begin{matrix}12+2\\7+4 \end{matrix}\right)=\left(\begin{matrix}14\\11\end{matrix}\right)

b)
\left(\begin{matrix}-16\\33 \end{matrix}\right)+\left(\begin{matrix}0,5\\-33 \end{matrix}\right)=\left(\begin{matrix}-16+0,5\\33+(-33) \end{matrix}\right)=\left(\begin{matrix}-15,5\\0 \end{matrix}\right)

c)
\left(\begin{matrix}-1,5\\\frac{1}{3} \end{matrix}\right)+\left(\begin{matrix}\sqrt{2}\\\pi\end{matrix}\right)=\left(\begin{matrix}-1,5+\sqrt{2}\\\frac{1}{3}+ \pi \end{matrix}\right)\approx \left(\begin{matrix}-0,086\\ 3,475 \end{matrix}\right)

d)  
\left(\begin{matrix}\frac{1}{2}\sqrt{2}\\5\pi \end{matrix}\right)-\left(\begin{matrix}\sqrt{2}\\\pi\end{matrix}\right)=\left(\begin{matrix}\frac{1}{2}\sqrt{2}-\sqrt{2}\\5\pi- \pi\end{matrix}\right)=\left(\begin{matrix}-\frac{1}{2}\sqrt{2}\\4\pi \end{matrix}\right) \approx \left(\begin{matrix}-0,707\\ 12,566 \end{matrix}\right)

e)  
\left(\begin{matrix}\frac{3}{7}\\5 \end{matrix}\right)+\left(\begin{matrix}\frac{5}{7}\\5 \end{matrix}\right)-\left(\begin{matrix}\frac{1}{7}\\5 \end{matrix}\right)=\left(\begin{matrix}\frac{3}{7}+\frac{5}{7}-\frac{1}{7}\\5+5-5 \end{matrix}\right)=\left(\begin{matrix}1 \\5\end{matrix}\right)

f)
\left(\begin{matrix}1\\7\\9 \end{matrix}\right)+\left(\begin{matrix}2\\4\\-1 \end{matrix}\right)=\left(\begin{matrix}1+2\\7+4\\9+(-1) \end{matrix}\right)=\left(\begin{matrix}3\\11\\8 \end{matrix}\right)

g)
\left(\begin{matrix}100\\71\\92 \end{matrix}\right)+\left(\begin{matrix}203\\4\\-119\end{matrix}\right)=\left(\begin{matrix}100+203\\71+4\\92+(-119) \end{matrix}\right)=\left(\begin{matrix}303\\75\\-27 \end{matrix}\right)

h)
\left(\begin{matrix}12,6\\8,1\\0,3\end{matrix}\right)-\left(\begin{matrix}-0,6\\0,9\\\frac{1}{3}\end{matrix}\right)=\left(\begin{matrix}12,6-(-0,6)\\8,1-0,9\\0,3-\frac{1}{3}\end{matrix}\right)=\left(\begin{matrix}13,2\\7,2\\-\frac{1}{30}\end{matrix}\right)

i)
\left(\begin{matrix}1\\0,5\\4\end{matrix}\right)-\left(\begin{matrix}-1\\0,5\\4\end{matrix}\right)+\left(\begin{matrix}-1\\-2\\20\end{matrix}\right)=\left(\begin{matrix}1-(-1)+(-1)\\0,5-0,5+(-2)\\4-4+20\end{matrix}\right)=\left(\begin{matrix}1\\-2\\20\end{matrix}\right)