Answer
Cramer's rule is not applicable.
Work Step by Step
The given system of equations is
$\left\{\begin{matrix}
x& -2y &+3z&=&1\\
3x& +y & -2z&=&0\\
2x& -4y &+6z &=&2
\end{matrix}\right.$
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.
