7.3-bo'lim : Kengaytirilgan matritsalar
3. Quyidagi kengaytirilgan matritsa uchun ko'rsatilgan elementar qator amallarini bajaring.
\[\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&7&{ - 2}&3\end{array}} \right]\]- \( - 9{R_{\,3}}\)
- \({R_{\,1}} \leftrightarrow {R_{\,2}}\)
- \({R_{\,3}} - {R_{\,1}} \to {R_{\,3}}\)
a Yechim
Ushbu operatsiya bizga kengaytirilgan matritsaning 3-qatoridagi barcha yozuvlarni -9 ga ko'paytirishni aytmoqda, shuning uchun buni qilaylik.
\[\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&7&{ - 2}&3\end{array}} \right]\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{ - 9{R_{\,3}}}\\ \to \end{array}\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&{ - 63}&{18}&{ - 27}\end{array}} \right]\]b Yechim
Ushbu operatsiya bizga kengaytirilgan matritsaning 1-qatori va 2-qatorini almashtirishni bildiradi. Mana o'sha ish.
\[\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&7&{ - 2}&3\end{array}} \right]\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{{R_{\,1}} \leftrightarrow {R_{\,2}}}\\ \to \end{array}\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{rrr|r}4&0&7&{ - 1}\\{10}&{ - 1}&{ - 5}&1\\0&7&{ - 2}&3\end{array}} \right]\]c Yechim
Ushbu operatsiyani bajarish uchun biz 3-qatorni 3-qatordagi asl yozuvlarni olish natijalari bilan almashtiramiz va ulardan 1-qatordagi yozuvlarni ayiramiz.
\[\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\0&7&{ - 2}&3\end{array}} \right]\,\,\,\,\,\,\,\,\,\,\begin{array}{*{20}{c}}{{R_{\,3}} - {R_{\,1}} \to {R_{\,3}}}\\ \to \end{array}\,\,\,\,\,\,\,\,\,\left[ {\begin{array}{rrr|r}{10}&{ - 1}&{ - 5}&1\\4&0&7&{ - 1}\\{ - 10}&8&3&2\end{array}} \right]\]Quyida ushbu operatsiya uchun individual hisob-kitoblar keltirilgan.
\[\begin{align*}& {\mbox{Column 1 }}:\,\,\,0 - \left( {10} \right) = - 10\\ & {\mbox{Column 2 }}:\,\,\,7 - \left( { - 1} \right) = 8\\ & {\mbox{Column 3 }}:\,\,\, - 2 - \left( { - 5} \right) = 3\\ & {\mbox{Column 4 }}:\,\,\,3 - \left( 1 \right) = 2\end{align*}\]