נתון:
בסיס סדור של R 2 {\displaystyle R^{2}} והבסיס סדור של C = { [ 1 1 ] , [ 2 1 ] } {\displaystyle C={\Biggl \{}\left[{\begin{matrix}1\\1\end{matrix}}\right],\left[{\begin{matrix}2\\1\end{matrix}}\right]{\Biggl \}}} ל- R 2 {\displaystyle R^{2}} . כמו גם העתקה לינארית T : R 2 → R 2 {\displaystyle T:R^{2}\rightarrow R^{2}} כך שהמטריצה מייצגת הינה: [ T ] B E = { [ 1 10 5 − 1 ] } {\displaystyle [T]_{B}^{E}={\Biggl \{}\left[{\begin{matrix}1&10\\5&-1\end{matrix}}\right]{\Biggl \}}} בנוסף נתון כי [ 1 2 ] {\displaystyle \left[{\begin{matrix}1\\2\end{matrix}}\right]} . מצא את [ v ] B {\displaystyle [v]_{B}}
[ T ( v ) ] c = [ 1 10 5 − 1 ] [ 1 2 ] = [ 21 3 ] {\displaystyle [T(v)]_{c}=\left[{\begin{matrix}1&10\\5&-1\end{matrix}}\right]\left[{\begin{matrix}1\\2\end{matrix}}\right]=\left[{\begin{matrix}21\\3\end{matrix}}\right]}
נמצא את T ( v ) {\displaystyle T(v)} :
T ( v ) = 21 ∗ [ 1 1 ] + 3 ∗ [ 2 1 ] = [ 24 27 ] {\displaystyle T(v)=21*\left[{\begin{matrix}1\\1\end{matrix}}\right]+3*\left[{\begin{matrix}2\\1\end{matrix}}\right]=\left[{\begin{matrix}24\\27\end{matrix}}\right]}
![{\displaystyle [t(v)]_{c}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/27e100f32154f9572ffaada0e3c86243cb30a2cc)
![{\displaystyle C={\Biggl \{}\left[{\begin{matrix}1\\1\end{matrix}}\right],\left[{\begin{matrix}2\\1\end{matrix}}\right]{\Biggl \}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/280b191c9b57e1ab7d40ca5a18c5c54fc1b1133b)
![{\displaystyle [T]_{B}^{E}={\Biggl \{}\left[{\begin{matrix}1&10\\5&-1\end{matrix}}\right]{\Biggl \}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/700576ce4b3edb4c0daa6f1b932484d2d59463e5)
![{\displaystyle \left[{\begin{matrix}1\\2\end{matrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0f23f57e7336da936480378528b1392e50565535)
![{\displaystyle [v]_{B}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a4793d2b632838429ce185dd247755f62786289)
![{\displaystyle [T(v)]_{c}=\left[{\begin{matrix}1&10\\5&-1\end{matrix}}\right]\left[{\begin{matrix}1\\2\end{matrix}}\right]=\left[{\begin{matrix}21\\3\end{matrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5912ec24e0c45fd0c4c4e6c9e2fde227cd3aa776)
![{\displaystyle T(v)=21*\left[{\begin{matrix}1\\1\end{matrix}}\right]+3*\left[{\begin{matrix}2\\1\end{matrix}}\right]=\left[{\begin{matrix}24\\27\end{matrix}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae533843c9c5a710ab326391751818d40d855729)