Ответы и объяснения

2014-01-17T15:06:38+00:00
Это матричное уравнение ХА=В, тогда  X=BA^{-1}
A=  \left(\begin{array}{ccc}2&1&3\\0&2&0\\1&4&5\end{array}\right)
A^{-1}= \frac{1}{\triangle A}  \left(\begin{array}{ccc}A_{11}&A_{21}&A_{31}\\A_{12}&A_{22}&A_{32}\\A_{13}&A_{23}&A_{33}\end{array}\right)
\triangle A=\left[\begin{array}{ccc}2&1&3\\0&2&0\\1&4&5\end{array}\right]=20-6=14
A_{11}=  \left[\begin{array}{cc}2&0\\4&5\end{array}\right]=10; A_{21}= -\left[\begin{array}{cc}1&3\\4&5\end{array}\right]=7;  
A_{31}= \left[\begin{array}{cc}1&3\\2&0\end{array}\right]=-6;
A_{12}= - \left[\begin{array}{cc}0&0\\1&5\end{array}\right]=0; A_{22}= \left[\begin{array}{cc}2&3\\1&5\end{array}\right]=7; 
A_{32}= -\left[\begin{array}{cc}2&3\\0&0\end{array}\right]=0;
A_{13}=  \left[\begin{array}{cc}0&2\\1&4\end{array}\right]=-2; A_{23}= -\left[\begin{array}{cc}2&1\\1&4\end{array}\right]=-7; 
A_{33}= \left[\begin{array}{cc}2&1\\0&2\end{array}\right]=4;
A^{-1}=\frac{1}{14}\left(\begin{array}{ccc}10&7&-6\\0&7&0\\-2&-7&4\end{array}\right)
X= \frac{1}{14} \left(\begin{array}{ccc}2&1&3\\0&2&0\\1&4&5\end{array}\right)* \left(\begin{array}{ccc}10&7&-6\\0&7&0\\-2&-7&4\end{array}\right)=
 =\frac{1}{14} \left(\begin{array}{ccc}4&0&6\\28&21&0\\54&42&-6\end{array}\right)