solve-using-matrix-method-x-y-4-2x-3y-5-

Question Number 37084 by Rio Mike last updated on 08/Jun/18

s o l v e u s i n g m a t r i x m e t h o d

x - y = 4

2 x - 3 y = 5

Commented by math khazana by abdo last updated on 09/Jun/18

(s) \Leftrightarrow (\begin{matrix} 1 - 1 \\ 2 - 3 \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 4 \\ 5 \end{matrix}) \Leftrightarrow A . (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 4 \\ 5 \end{matrix})

d e t A = - 1 \neq 0 \Rightarrow (\begin{matrix} x \\ y \end{matrix}) = A^{- 1} . (\begin{matrix} 4 \\ 5 \end{matrix})

A^{- 1} = \frac{t (c o m A)}{d e t A} w i t h c o m A = {(- 1)}^{i + j} A_{i j}

= (\begin{matrix} a_{11} a_{12} \\ a_{21} a_{22} \end{matrix}) = (\begin{matrix} - 3 - 2 \\ 1 1 \end{matrix}) a n d

t (c o m A) = (\begin{matrix} - 3 1 \\ - 2 1 \end{matrix}) \Rightarrow A^{- 1} = (\begin{matrix} 3 - 1 \\ 2 - 1 \end{matrix})

(\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 3 - 1 \\ 2 - 1 \end{matrix}) (\begin{matrix} 4 \\ 5 \end{matrix}) = (\begin{matrix} 7 \\ 3 \end{matrix}) \Rightarrow x = 7 a n d y = 3

Commented by math khazana by abdo last updated on 09/Jun/18

t h i s m e t h o d i s g e n e r a l f o r n u n k n o w n (x_{i}) i f

t h e m a t r i x A i s i n v e r s i b l e .