macierz przekształcenia w bazie
: 2 sty 2012, o 22:12
Znajdź macierz tego przekształcenia w bazie {[0, 0, 1}, [1, 0, 1], [1, 1, 1]}.
czy dobrze to rozpisałem?
\(\displaystyle{ f(\varepsilon _1)=f(\left[\begin{array}{c}1\\0\\0\end{array}\right])=\left[\begin{array}{c}3\\0\\-3\end{array}\right]=3\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+3\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+(-3)\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]
f(\varepsilon _2)=f(\left[\begin{array}{c}0\\1\\0\end{array}\right])=\left[\begin{array}{c}2\\1\\2\end{array}\right]=1\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+(-1)\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+2\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]
f(\varepsilon _3)=f(\left[\begin{array}{c}0\\0\\1\end{array}\right])=\left[\begin{array}{c}1\\2\\1\end{array}\right]=(-1)\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+1\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+1\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]}\)
czy dobrze to rozpisałem?
\(\displaystyle{ f(\varepsilon _1)=f(\left[\begin{array}{c}1\\0\\0\end{array}\right])=\left[\begin{array}{c}3\\0\\-3\end{array}\right]=3\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+3\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+(-3)\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]
f(\varepsilon _2)=f(\left[\begin{array}{c}0\\1\\0\end{array}\right])=\left[\begin{array}{c}2\\1\\2\end{array}\right]=1\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+(-1)\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+2\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]
f(\varepsilon _3)=f(\left[\begin{array}{c}0\\0\\1\end{array}\right])=\left[\begin{array}{c}1\\2\\1\end{array}\right]=(-1)\cdot \left[\begin{array}{c}1\\0\\0\end{array}\right]+1\cdot \left[\begin{array}{c}1\\1\\0\end{array}\right]+1\cdot \left[\begin{array}{c}1\\1\\1\end{array}\right]}\)