Solve the following system of linear equations using the n by n or m by n Gaussian method.

Without the specific equations provided, I am unable to solve the system of linear equations using the Gaussian method. Please provide the equations so that I can assist you further.

$$\begin{split} x_1+2x_2-3x_3&=0 \\\ 2x_1+5x_2-7x_3&=0 \\\ 3x_1+7x_2-10x_3&=0\end{split}$$

First, write the corresponding augmented matrix and row operate it into an echelon form.
$$\begin{split} \left[\begin{array}{rrr|r} 1 & 2 & -3 & 0 \\\ 2 & 5 & -7 & 0 \\\ 3 & 7 & -10 & 0\end{array}\right] \rightarrow \left[\begin{array}{rrr|r} 1 & 2 & -3 & 0 \\\ 0 & 1 & -1 & 0 \\\ 0 & 1 & -1 & 0\end{array}\right] \\\ \rightarrow \left[\begin{array}{rrr|r} 1 & 0 & 0 & 0 \\\ 0 & 1 & 0 & 0 \\\ 0 & 0 & 0 & 0\end{array}\right] \end{split}$$

Hence, the system is inconsistent.