جواب کار در کلاس صفحه 15 درس 1 هندسه دوازدهم (ماتریس و کاربردها)

الف \(- 1 \times \left[ {\begin{array}{*{20}{c}}1&2&3\\4&5&6\\{ - 4}&{ - 5}&{ - 6}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - 1}&{ - 2}&{ - 3}\\{ - 4}&{ - 5}&{ - 6}\\4&5&6\end{array}} \right]\)

ب \(\frac{1}{2} \times \left[ {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}4&6&8&1\end{array}}\\{\begin{array}{*{20}{c}}0&3&5&7\end{array}}\\{\begin{array}{*{20}{c}}{\sqrt 2 }&{ - 1}&2&8\end{array}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}2&3&4&{\frac{1}{2}}\\0&{\frac{3}{2}}&{\frac{5}{2}}&{\frac{7}{2}}\\{\frac{{\sqrt 2 }}{2}}&{ - \frac{1}{2}}&1&4\end{array}} \right]\)

پ \(0 \times \left[ {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}1&2&{ - 1}\end{array}}\\{\begin{array}{*{20}{c}}{ - 2}&{ - 3}&{ - 4}\end{array}}\\{\begin{array}{*{20}{c}}5&6&7\end{array}}\\{\begin{array}{*{20}{c}}1&1&0\end{array}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0&0&0\\0&0&0&0\\0&0&0&0\\0&0&0&0\end{array}} \right]\)

ت \(7 \times \left[ {\begin{array}{*{20}{c}}{\begin{array}{*{20}{c}}0&0&0\end{array}}\\{\begin{array}{*{20}{c}}0&0&0\end{array}}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}0&0&0\\0&0&0\end{array}} \right]\)

\(\begin{array}{l}\left[ {\begin{array}{*{20}{c}}2&4&6\\8&4&2\\{10}&3&1\end{array}} \right] = 2 \times \left[ {\begin{array}{*{20}{c}}1&2&3\\4&2&1\\5&{\frac{3}{2}}&{\frac{1}{2}}\end{array}} \right]\\\\\left[ {\begin{array}{*{20}{c}}1&{ - 1}&{ - 2}\\3&1&4\\2&5&0\end{array}} \right] = \left( { - 1} \right) \times \left[ {\begin{array}{*{20}{c}}{ - 1}&1&2\\{ - 3}&{ - 1}&{ - 4}\\{ - 2}&{ - 5}&0\end{array}} \right]\end{array}\)