Question

помогите решить уравнение

Answer 1

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