सोडोवचें {ccc}{6}&{0}&{-6}{-4}&{2}&{3}{0}&{-1}&{6}{l}{x_{1}}{x_{2}}{x_{3}}={c}{3}{-6}{0}

$$\left( \begin{array} { c c c } { 6 } & { 0 } & { - 6 } \\ { - 4 } & { 2 } & { 3 } \\ { 0 } & { - 1 } & { 6 } \end{array} \right) \left( \begin{array} { l } { x _ { 1 } } \\ { x _ { 2 } } \\ { x _ { 3 } } \end{array} \right) = \left( \begin{array} { c } { 3 } \\ { - 6 } \\ { 0 } \end{array} \right)$$

x_1, x_3, x_2 खातीर सोडोवचें

$$x_{1}=\frac{3}{22}\approx 0.136363636$$

$$x_{3}=-\frac{4}{11}\approx -0.363636364$$

$$x_{2} = -\frac{24}{11} = -2\frac{2}{11} \approx -2.181818182$$

बदली वापरून संक्षिप्त पांवडे

समिकरणांचो क्रम परत लावचो.

$$-x_{2}+6x_{3}=0 -4x_{1}+2x_{2}+3x_{3}=-6 6x_{1}-6x_{3}=3$$

x_{2} खातीर -x_{2}+6x_{3}=0 सोडोवचो.

$$x_{2}=6x_{3}$$

-4x_{1}+2x_{2}+3x_{3}=-6 ह्या समिकरणांत x_{2} खातीर 6x_{3} बदलपी घेवचो.

$$-4x_{1}+2\times 6x_{3}+3x_{3}=-6$$

x_{3} खातीर दुसरें समिकरण आनी x_{1} खातीर तिसरें समिकरण सोडोवचें.

$$x_{3}=-\frac{2}{5}+\frac{4}{15}x_{1} x_{1}=\frac{1}{2}+x_{3}$$

x_{1}=\frac{1}{2}+x_{3} ह्या समिकरणांत x_{3} खातीर -\frac{2}{5}+\frac{4}{15}x_{1} बदलपी घेवचो.

$$x_{1}=\frac{1}{2}-\frac{2}{5}+\frac{4}{15}x_{1}$$

x_{1} खातीर x_{1}=\frac{1}{2}-\frac{2}{5}+\frac{4}{15}x_{1} सोडोवचो.

$$x_{1}=\frac{3}{22}$$

x_{3}=-\frac{2}{5}+\frac{4}{15}x_{1} ह्या समिकरणांत x_{1} खातीर \frac{3}{22} बदलपी घेवचो.

$$x_{3}=-\frac{2}{5}+\frac{4}{15}\times \frac{3}{22}$$

x_{3}=-\frac{2}{5}+\frac{4}{15}\times \frac{3}{22} तल्यान x_{3} मेजचो.

$$x_{3}=-\frac{4}{11}$$

x_{2}=6x_{3} ह्या समिकरणांत x_{3} खातीर -\frac{4}{11} बदलपी घेवचो.

$$x_{2}=6\left(-\frac{4}{11}\right)$$

x_{2}=6\left(-\frac{4}{11}\right) तल्यान x_{2} मेजचो.

$$x_{2}=-\frac{24}{11}$$

प्रणाली आतां सुटावी जाली.

$$x_{1}=\frac{3}{22} x_{3}=-\frac{4}{11} x_{2}=-\frac{24}{11}$$