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5: Система рівнянь
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.05%3A_%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B0_%D1%80%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D1%8C
\[\begin{bmatrix} a_{11} & a_{12} & \cdot & \cdot & a_{1n} \\ a_{21} & a_{22} & \cdot & \cdot & a_{2n} \\ \cdot & \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot & \cdot \\ a_{n1} & a_{... $\begin{bmatrix} a_{11} & a_{12} & \cdot & \cdot & a_{1n} \\ a_{21} & a_{22} & \cdot & \cdot & a_{2n} \\ \cdot & \cdot & \cdot & \cdot & \cdot \\ \cdot & \cdot & \cdot & \cdot & \cdot \\ a_{n1} & a_{n2} & \cdot & \cdot & a_{nn} \\ \end{bmatrix}\begin{bmatrix} a_{11}^{'} \\ a_{21}^{'} \\ \cdot \\ \cdot \\ a_{n1}^{'} \\ \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ \cdot \\ \cdot \\ 0 \\ \end{bmatrix} \nonumber$
1: Вступ
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.01%3A_%D0%92%D1%81%D1%82%D1%83%D0%BF
\[\lbrack A\rbrack = \begin{bmatrix} a_{11} & a_{12} & {.......} & a_{1n} \\ a_{21} & a_{22} & {.......} & a_{2n} \\ \vdots & & & \vdots \\ a_{m1} & a_{m2} & {.......} & a_{mn} \\ \end{bmatrix}\nonumb... $\lbrack A\rbrack = \begin{bmatrix} a_{11} & a_{12} & {.......} & a_{1n} \\ a_{21} & a_{22} & {.......} & a_{2n} \\ \vdots & & & \vdots \\ a_{m1} & a_{m2} & {.......} & a_{mn} \\ \end{bmatrix}\nonumber$ $\left|a_{11}\right|=\left|25\right| ,\left|a_{12}\right|+\left|a_{13}\right|=|5|+|1|=6,25 \geq 6\nonumber$ $\left|a_{33}\right|=|6|\left|a_{31}\right|+\left|a_{32}\right|=|3|+|2|=5,6>5\nonumber$ б) Матриця
4: Операції унарної матриці
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.04%3A_%D0%9E%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%96%D1%97_%D1%83%D0%BD%D0%B0%D1%80%D0%BD%D0%BE%D1%97_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%86%D1%96
\[\begin{split} \left\lbrack A \right\rbrack &= \left\lbrack \begin{matrix} 25 \\ 5 \\ 6 \\ \end{matrix}\begin{matrix} 20 \\ 10 \\ 16 \\ \end{matrix}\begin{matrix} 3 \\ 15 \\ 7 \\ \end{matrix}\begin{m...\[\begin{split} \left\lbrack A \right\rbrack &= \left\lbrack \begin{matrix} 25 \\ 5 \\ 6 \\ \end{matrix}\begin{matrix} 20 \\ 10 \\ 16 \\ \end{matrix}\begin{matrix} 3 \\ 15 \\ 7 \\ \end{matrix}\begin{matrix} 2 \\ 25 \\ 27 \\ \end{matrix} \right\rbrack\\ &= \left\lbrack \begin{matrix} 33.25 \\ 40.19 \\ 25.03 \\ \end{matrix}\begin{matrix} 30.01 \\ 38.02 \\ 22.02 \\ \end{matrix}\begin{matrix} 35.02 \\ 41.03 \\ 27.03 \\ \end{matrix}\begin{matrix} 30.05 \\ 38.23 \\ 22.95 \\ \end{matrix} \right\rbrack…
Індекс
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/zz%3A_%D0%9D%D0%B0%D0%B7%D0%B0%D0%B4_%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D1%96%D1%8F/10%3A_%D0%86%D0%BD%D0%B4%D0%B5%D0%BA%D1%81
Template:DynamicIndex
9: Адекватність рішень
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.09%3A_%D0%90%D0%B4%D0%B5%D0%BA%D0%B2%D0%B0%D1%82%D0%BD%D1%96%D1%81%D1%82%D1%8C_%D1%80%D1%96%D1%88%D0%B5%D0%BD%D1%8C
\[\begin{split} \left\| A \right\|_{\infty} &= \begin{matrix} \max \\ 1 \leq i \leq 3 \\ \end{matrix}\sum_{j = 1}^{3}\left| a_{ij} \right|\\ &= max\left\lbrack \left( \left| 10 \right| + \left| - 7 \r...\[\begin{split} \left\| A \right\|_{\infty} &= \begin{matrix} \max \\ 1 \leq i \leq 3 \\ \end{matrix}\sum_{j = 1}^{3}\left| a_{ij} \right|\\ &= max\left\lbrack \left( \left| 10 \right| + \left| - 7 \right| + \left| 0 \right| \right),\left( \left| - 3 \right| + \left| 2.099 \right| + \left| 6 \right| \right),\left( \left| 5 \right| + \left| - 1 \right| + \left| 5 \right| \right) \right\rbrack\\ &= max\left\lbrack \left( 10 + 7 + 0 \right),\left( 3 + 2.099 + 6 \right),\left( 5 + 1 + 5 \right) \ri…
7: Метод розкладання LU для розв'язання одночасних лінійних рівнянь
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.07%3A_%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D1%80%D0%BE%D0%B7%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D1%8F_LU_%D0%B4%D0%BB%D1%8F_%D1%80%D0%BE%D0%B7%D0%B2'%D1%8F%D0%B7%D0%B0%D0%BD%D0%BD%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%87%D0%B0%D1%81%D0%BD%D0%B8%D1%85_%D0%BB%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B8%D1%85_%D1%80%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D1%8C
\[\left\lbrack I \right\rbrack \left\lbrack U \right\rbrack \left\lbrack X \right\rbrack = \left\lbrack L \right\rbrack^{- 1}\left\lbrack C \right\rbrack\ \text{as }\left( \left\lbrack L \right\rbrack... $\left\lbrack I \right\rbrack \left\lbrack U \right\rbrack \left\lbrack X \right\rbrack = \left\lbrack L \right\rbrack^{- 1}\left\lbrack C \right\rbrack\ \text{as }\left( \left\lbrack L \right\rbrack^{- 1}\left\lbrack L \right\rbrack = \lbrack I\rbrack \right) \nonumber$
6: Метод гаусової елімінації для вирішення одночасних лінійних рівнянь
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.06%3A_%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%B3%D0%B0%D1%83%D1%81%D0%BE%D0%B2%D0%BE%D1%97_%D0%B5%D0%BB%D1%96%D0%BC%D1%96%D0%BD%D0%B0%D1%86%D1%96%D1%97_%D0%B4%D0%BB%D1%8F_%D0%B2%D0%B8%D1%80%D1%96%D1%88%D0%B5%D0%BD%D0%BD%D1%8F_%D0%BE%D0%B4%D0%BD%D0%BE%D1%87%D0%B0%D1%81%D0%BD%D0%B8%D1%85_%D0%BB%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B8%D1%85_%D1%80%D1%96%D0%B2%D0%BD%D1%8F%D0%BD%D1%8C
\[\begin{split} &a_{11}x_{1} + a_{12}x_{2} + a_{13}x_{3} + \ldots + a_{1n}x_{n} = b_{1}\\ &{a^\prime }_{22}x_{2} + {a^\prime }_{23}x_{3} + \ldots + {a^\prime }_{2n}x_{n} = {b^\prime }_{2}\\ &{a^\prime...\[\begin{split} &a_{11}x_{1} + a_{12}x_{2} + a_{13}x_{3} + \ldots + a_{1n}x_{n} = b_{1}\\ &{a^\prime }_{22}x_{2} + {a^\prime }_{23}x_{3} + \ldots + {a^\prime }_{2n}x_{n} = {b^\prime }_{2}\\ &{a^\prime }_{32}x_{2} + {a^\prime }_{33}x_{3} + \ldots + {a^\prime }_{3n}x_{n} = {b^\prime }_{3}\\ &\vdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vdots \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \vdots\\ &{a^\prime }_{n2}x_{2} + {a^\prime }_{n3}x_{3} + \ldots + {a^\prime }_{\text{nn}}x_{n} = {b^\prime }_{n} \end…
8: Метод Гаусса-Зайделя
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.08%3A_%D0%9C%D0%B5%D1%82%D0%BE%D0%B4_%D0%93%D0%B0%D1%83%D1%81%D1%81%D0%B0-%D0%97%D0%B0%D0%B9%D0%B4%D0%B5%D0%BB%D1%8F
$\begin{bmatrix} x_{1} & x_{2} & x_{3} \\ \end{bmatrix} = \begin{bmatrix} 0.90666 & -1.0115 & -1.0243 \\ \end{bmatrix}$ \({\begin{bmatrix} \left| \in_{a} \right|_{1} & \left| \in_{a} \right|_{2} & \l... $\begin{bmatrix} x_{1} & x_{2} & x_{3} \\ \end{bmatrix} = \begin{bmatrix} 0.90666 & -1.0115 & -1.0243 \\ \end{bmatrix}$ ${\begin{bmatrix} \left| \in_{a} \right|_{1} & \left| \in_{a} \right|_{2} & \left| \in_{a} \right|_{3} \\ \end{bmatrix} = \begin{bmatrix} 65.001\% & 10.564\% & 17.099\% \\ \end{bmatrix} }$ \({\begin{bmatrix} \left| \in_{a} \right|_{1} & \left| \in_{a} \right|_{2} & \left| \in_{a} \right|_{3} \\ \end{bmatrix} = \begin{bmatrix} 65.001\% & 10.564\% & 17.099\% \\ \end{bmatrix} }…
2: Вектори
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.02%3A_%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8
\[\begin{split} \lbrack A\rbrack + \lbrack B\rbrack &= \begin{bmatrix} a_{1} \\ a_{2} \\ \vdots \\ a_{n} \\ \end{bmatrix} + \begin{bmatrix} b_{1} \\ b_{2} \\ \vdots \\ b_{n} \\ \end{bmatrix}\\ &= \beg... $\begin{split} \lbrack A\rbrack + \lbrack B\rbrack &= \begin{bmatrix} a_{1} \\ a_{2} \\ \vdots \\ a_{n} \\ \end{bmatrix} + \begin{bmatrix} b_{1} \\ b_{2} \\ \vdots \\ b_{n} \\ \end{bmatrix}\\ &= \begin{bmatrix} a_{1} + b_{1} \\ a_{2} + b_{2} \\ \vdots \\ a_{n} + b_{n} \\ \end{bmatrix} \end{split}\notag$
10: Власні значення та власні вектори
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/01%3A_%D0%93%D0%BB%D0%B0%D0%B2%D0%B8/1.10%3A_%D0%92%D0%BB%D0%B0%D1%81%D0%BD%D1%96_%D0%B7%D0%BD%D0%B0%D1%87%D0%B5%D0%BD%D0%BD%D1%8F_%D1%82%D0%B0_%D0%B2%D0%BB%D0%B0%D1%81%D0%BD%D1%96_%D0%B2%D0%B5%D0%BA%D1%82%D0%BE%D1%80%D0%B8
\[\begin{split} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \\ \end{bmatrix} &= \begin{bmatrix} - a \\ b \\ a \\ \end{bmatrix}\\ & = \begin{bmatrix} - a \\ 0 \\ a \\ \end{bmatrix} + \begin{bmatrix} 0 \\ b... $\begin{split} \begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \\ \end{bmatrix} &= \begin{bmatrix} - a \\ b \\ a \\ \end{bmatrix}\\ & = \begin{bmatrix} - a \\ 0 \\ a \\ \end{bmatrix} + \begin{bmatrix} 0 \\ b \\ 0 \\ \end{bmatrix}\\ &= a\begin{bmatrix} - 1 \\ 0 \\ 1 \\ \end{bmatrix} + b\begin{bmatrix} 0 \\ 1 \\ 0 \\ \end{bmatrix} \end{split} \nonumber$
Передня матерія
https://ukrayinska.libretexts.org/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0/%D0%9B%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%92%D1%81%D1%82%D1%83%D0%BF_%D0%B4%D0%BE_%D0%BC%D0%B0%D1%82%D1%80%D0%B8%D1%87%D0%BD%D0%BE%D1%97_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8_(Kaw)/00%3A_%D0%9F%D0%B5%D1%80%D0%B5%D0%B4%D0%BD%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D1%80%D1%96%D1%8F