Да се намери обратната матрица чрез елементарни образувания

[shener.hadjimehmed]

22751045_1486639011374029_204358964_o.jpg (94.17 KiB) Прегледано 414 пъти

[aifC]

A = [tex]\begin{pmatrix}0 & 2 & 0 \\ 0 & 0 & 3 \\ 1 & 0 & 0 \end{pmatrix} \Rightarrow \begin{pmatrix}0 & 2 & 0 & 1 & 0 & 0 \\ 0 & 0 & 3 & 0 & 1 & 0 \\ 1 & 0 & 0 & 0 & 0 & 1 \end{pmatrix}[/tex] [tex]R_{3} \Leftrightarrow R{1}[/tex] [tex]\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 3 & 0 & 1 & 0 \\ 0 & 2 & 0 & 1 & 0 & 0 \end{pmatrix}[/tex] [tex]R_{3} \Leftrightarrow R_{2}[/tex]

[tex]\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 2 & 0 & 1 & 0 & 0\\ 0 & 0 & 3 & 0 & 1 & 0 \end{pmatrix}[/tex] [tex]\frac{1}{2}*R_{2}/2 \rightarrow R_{2}[/tex] [tex]\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 1 \\ 0 & 1 & 0 & \frac{1}{2} & 0 & 0\\ 0 & 0 & 3 & 0 & 1 & 0 \end{pmatrix}[/tex] [tex]\frac{1}{3}*R_{3}/3 \rightarrow R_{3}[/tex] [tex]\Rightarrow A^{-1} = \begin{pmatrix}0 & 0 & 1 \\ \frac{1}{2} & 0 & 0 \\ 0 & \frac{1}{3} & 0 \end{pmatrix}[/tex]