Question

помогите решить уравнение

Answer 1

$\displaystyle \\ \begin{cases}& 2x_{1}-3x_{2}=-4\\& 4x_{1}-x_{2}=2\end{cases}\\\\\\ A=\begin{pmatrix}2&-3\\4&-1\end{pmatrix} \;\;\; B=\binom{-4}{2} \;\;\; X=\binom{x_{1}}{x_{2}}\\\\ AX=B \Rightarrow A^{-1}AX=A^{-1}B\Rightarrow EX=A^{-1}B \Rightarrow \mathbf{X=A^{-1}B}\\\\ |A|=\begin{vmatrix} 2&-3\\ 4&-1 \end{vmatrix}=-2+12=10\\\\ A_{11}=-1,\; A_{12}=-4,\; A_{21}=3,\; A_{22}=2\\\\ \tilde{A}=\begin{pmatrix}-1&-4\\3&2\end{pmatrix}, \;\; \tilde{A}^{T}=\begin{pmatrix}-1&3\\-4&2\end{pmatrix}\\\\ A^{-1}={1\over10}\begin{pmatrix}-1&3\\-4&2\end{pmatrix}\\\\ X={1\over10}\begin{pmatrix}-1&3\\-4&2\end{pmatrix}\binom{-4}{2}={1\over10}\binom{10}{20}=\binom{1}{2}\\\\ \mathbf{x_{1}=1}\\ \mathbf{x_{2}=2}$