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Научный форум dxdyМатематика, Физика, Computer Science, Machine Learning, LaTeX, Механика и Техника, Химия,Биология и Медицина, Экономика и Финансовая Математика, Гуманитарные науки |
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| Страница 1 из 1 |
[ Сообщений: 9 ] |
23.03.2013, 17:53 
![$\[\left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}} + {a_{1,2}}}&{...}&{a_{1,n - 1} + a_{1,n}} \\
{a_{2,1}}&{a_{2,1} + a_{2,2}}&{...}&{a_{2,n - 1} + a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1} + a_{n,2}}&{...}&{{a_{n,n - 1}} + {a_{n,n}}}
\end{array}} \right|\]$](https://dxdy-03.korotkov.co.uk/f/6/9/3/693dda53cf7eca0402f7e6a4f1d0b18182.png "$\[\left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}} + {a_{1,2}}}&{...}&{a_{1,n - 1} + a_{1,n}} \\
{a_{2,1}}&{a_{2,1} + a_{2,2}}&{...}&{a_{2,n - 1} + a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1} + a_{n,2}}&{...}&{{a_{n,n - 1}} + {a_{n,n}}}
\end{array}} \right|\]$")
![$\[\left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,2}}}&{...}&{a1,n} \\
{a_{2,1}}&{a_{2,2}}&{...}&{a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,2}}&{...}&{{a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}}}&{...}&{{a_{1,n}}} \\
{{a_{2,1}}}&{{a_{2,2}}}&{...}&{{a_{2,n}}} \\
{...}&{...}&{...}&{...} \\
{{a_{n,1}}}&{{a_{n,2}}}&{...}&{{a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}}}&{...}&{a_{1,n - 1} + a_{1,n}} \\
{a_{2,1}}&{a_{2,1}}&{...}&{a_{2,n - 1} + a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1}}&{...}&{{a_{n,n - 1}} + {a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}} + {a_{1,2}}}&{...}&{a_{1,n - 1}}&{a_{1,n - 1}}&{{a_{1,n}}} \\
{a_{2,1}}&{a_{2,1} + a_{2,2}}&{...}&{a_{2,n - 1}}&{a_{2,n - 1}}&{{a_{2,n}}} \\
{...}&{...}&{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1} + a_{n,2}}&{...}&{{a_{n,n - 1}}}&{{a_{n,n - 1}}}&{{a_{n,n}}}
\end{array}} \right| = \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,2}}}&{...}&{a_{1,n}} \\
{a_{2,1}}&{a_{2,2}}&{...}&{a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,2}}&{...}&{{a_{n,n}}}
\end{array}} \right|\]$](https://dxdy-02.korotkov.co.uk/f/1/d/1/1d157e0e5f221e11c51d8486f94fd22982.png "$\[\left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,2}}}&{...}&{a1,n} \\
{a_{2,1}}&{a_{2,2}}&{...}&{a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,2}}&{...}&{{a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}}}&{...}&{{a_{1,n}}} \\
{{a_{2,1}}}&{{a_{2,2}}}&{...}&{{a_{2,n}}} \\
{...}&{...}&{...}&{...} \\
{{a_{n,1}}}&{{a_{n,2}}}&{...}&{{a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}}}&{...}&{a_{1,n - 1} + a_{1,n}} \\
{a_{2,1}}&{a_{2,1}}&{...}&{a_{2,n - 1} + a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1}}&{...}&{{a_{n,n - 1}} + {a_{n,n}}}
\end{array}} \right| + \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,1}} + {a_{1,2}}}&{...}&{a_{1,n - 1}}&{a_{1,n - 1}}&{{a_{1,n}}} \\
{a_{2,1}}&{a_{2,1} + a_{2,2}}&{...}&{a_{2,n - 1}}&{a_{2,n - 1}}&{{a_{2,n}}} \\
{...}&{...}&{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,1} + a_{n,2}}&{...}&{{a_{n,n - 1}}}&{{a_{n,n - 1}}}&{{a_{n,n}}}
\end{array}} \right| = \left| {\begin{array}{*{20}{c}}
{{a_{1,1}}}&{{a_{1,2}}}&{...}&{a_{1,n}} \\
{a_{2,1}}&{a_{2,2}}&{...}&{a_{2,n}} \\
{...}&{...}&{...}&{...} \\
{a_{n,1}}&{a_{n,2}}&{...}&{{a_{n,n}}}
\end{array}} \right|\]$")
. После прибавления к последнему столцу матрицы 
, причем по указанному свойству 
. Далее к предпоследнему столбцу матрицы 