مقدار بردار مجهول را بیابید. \(\begin{array}{l}1)\,\,2\vec x + \vec i = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right]\\\\2)\,\,\vec i + \vec x = \left[ {\begin{array}{*{20}{c}}3\\5\end{array}} \right]\\\\3)\,\,3\vec i + 2\vec j + 2\vec x = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right]\end{array}\)  

\(\begin{array}{l}1)\,\,2\vec x + \vec i = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] \Rightarrow 2\vec x = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] - \vec i = \\\left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}1\\0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}4\\6\end{array}} \right] \Rightarrow \vec x\frac{1}{2}\left[ {\begin{array}{*{20}{c}}4\\6\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}2\\3\end{array}} \right]\\\\2)\,\,\vec i + \vec x = \left[ {\begin{array}{*{20}{c}}3\\5\end{array}} \right] \Rightarrow \vec x = \left[ {\begin{array}{*{20}{c}}3\\5\end{array}} \right] - \vec i = \left[ {\begin{array}{*{20}{c}}3\\5\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}1\\0\end{array}} \right]\\ \Rightarrow \vec x = \left[ {\begin{array}{*{20}{c}}2\\5\end{array}} \right]\\\\3)\,\,3\vec i + 2\vec j + 2\vec x = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] \Rightarrow 2\vec x = \left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] - 3\vec i - 2\vec j = \\\left[ {\begin{array}{*{20}{c}}5\\6\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}3\\0\end{array}} \right] - \left[ {\begin{array}{*{20}{c}}0\\2\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}2\\4\end{array}} \right] \Rightarrow \vec x = \frac{1}{2}\left[ {\begin{array}{*{20}{c}}2\\4\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}1\\2\end{array}} \right]\end{array}\)