Solving systems of linear equations using Cramer's rule
Consider system of linear equations in x ,y ,z
\[a_1x+b_1y+c_1z=d_1\]
\[a_2x+b_2y+c_2z=d_2\]
\[a_3x+b_3y+c_3z=d_3\]
\[ \Delta \] is defined as \[ \begin{bmatrix} a_1& b_1 &c_1 \\ a_2& b_2 &c_2 \\a_3 &b_3 & c_3 \\ \end{bmatrix}\]
\[ \Delta _1=\begin{bmatrix} d_1& b_1 &c_1 \\ d_2& b_2 &c_2 \\d_3 &b_3 & c_3 \\ \end{bmatrix}\]
\[ \Delta _2=\begin{bmatrix} a_1& d_1 &c_1 \\ a_2& d_2 &c_2 \\a_3 &d_3 & c_3 \\ \end{bmatrix}\]
\[ \Delta _3=\begin{bmatrix} a_1& b_1 &d_1 \\ a_2& b_2 &d_2 \\a_3 &b_3 & d_3 \\ \end{bmatrix}\]
x , y, z can be calculated as
\[ x=\frac{ \Delta_1 }{ \Delta }\]
\[ y=\frac{ \Delta_2 }{ \Delta }\]
\[ z=\frac{ \Delta_3 }{ \Delta }\]
