Answer
Cramer's rule is not applicable.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
x& -2y &+3z&=&0\\
3x&+y & -2z&=&0\\
2x& -4y &+6z &=&0
\end{matrix}\right.$
The formula to determine the determinant is
$D=\begin{vmatrix}
a& b &c \\
d& e &f \\ g &h &i \end{vmatrix}=a\begin{vmatrix}
e& f \\ h&i \end{vmatrix}-b\begin{vmatrix}
d& f \\ g&i \end{vmatrix}+c\begin{vmatrix}
d& e \\ g&h \end{vmatrix}$
Determinant $D$ consists of the $x,y$ and $z$ coefficients.
$D=\begin{vmatrix}
1& -2 &3 \\
3& 1 &-2\\
2 &-4 &6
\end{vmatrix}=0$
We have $D=0$.
Hence, the Cramer's rule is not applicable.
