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

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

Datrys ar gyfer x_1, x_3, x_2

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

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

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

Camau Byr wrth Ddefnyddio Amnewid

Newid trefn yr hafaliadau.

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

Datrys -x_{2}+6x_{3}=0 ar gyfer x_{2}.

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

Amnewid 6x_{3} am x_{2} yn yr hafaliad -4x_{1}+2x_{2}+3x_{3}=-6.

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

Datrys yr ail hafaliad ar gyfer x_{3} a'r trydydd hafaliad ar gyfer x_{1}.

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

Amnewid -\frac{2}{5}+\frac{4}{15}x_{1} am x_{3} yn yr hafaliad x_{1}=\frac{1}{2}+x_{3}.

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

Datrys x_{1}=\frac{1}{2}-\frac{2}{5}+\frac{4}{15}x_{1} ar gyfer x_{1}.

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

Amnewid \frac{3}{22} am x_{1} yn yr hafaliad x_{3}=-\frac{2}{5}+\frac{4}{15}x_{1}.

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

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

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

Amnewid -\frac{4}{11} am x_{3} yn yr hafaliad x_{2}=6x_{3}.

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

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

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

Mae’r system wedi’i datrys nawr.

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