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Question Number 112904 by mohammad17 last updated on 10/Sep/20

solve the equation y+x=3, 2y+x=5 by ussing matrixis method  help me sir please ?

$${solve}\:{the}\:{equation}\:{y}+{x}=\mathrm{3},\:\mathrm{2}{y}+{x}=\mathrm{5}\:{by}\:{ussing}\:{matrixis}\:{method} \\ $$$${help}\:{me}\:{sir}\:{please}\:? \\ $$

Answered by bemath last updated on 10/Sep/20

 (((1   1)),((1   2)) ) ((x),(y) )= ((3),(5) )   ((x),(y) )= (((1   1)),((1   2)) )^(−1)  ((3),(5) )          = (1/1) (((2     −1)),((−1    1)) ) ((3),(5) )          = (((    6−5)),((−3+5)) )= ((1),(2) )

$$\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\mathrm{2}}\end{pmatrix}\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\begin{pmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{pmatrix} \\ $$$$\begin{pmatrix}{\mathrm{x}}\\{\mathrm{y}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\mathrm{2}}\end{pmatrix}^{−\mathrm{1}} \begin{pmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{1}}\begin{pmatrix}{\mathrm{2}\:\:\:\:\:−\mathrm{1}}\\{−\mathrm{1}\:\:\:\:\mathrm{1}}\end{pmatrix}\begin{pmatrix}{\mathrm{3}}\\{\mathrm{5}}\end{pmatrix} \\ $$$$\:\:\:\:\:\:\:\:=\begin{pmatrix}{\:\:\:\:\mathrm{6}−\mathrm{5}}\\{−\mathrm{3}+\mathrm{5}}\end{pmatrix}=\begin{pmatrix}{\mathrm{1}}\\{\mathrm{2}}\end{pmatrix} \\ $$

Commented by mohammad17 last updated on 10/Sep/20

thank you sir

$${thank}\:{you}\:{sir} \\ $$

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