Set of Linear equation has no solution or unique solution or infinite solution? For the system 
$$
\left\{
\begin{array}{rcrcrcr}
 x &+ &3y &-  &z &= &-4 \\
4x &-  &y &+ &2z &= &3 \\
2x &-  &y &- &3z &= &1
\end{array}
\right. 
$$
what is the condition to determine if there is no solution or unique solution or infinite solution? 
Thank you!

There is an easier way to determine whether a system of equations has unique, infinite or no solution. It is as follows: calculate determinant $D$ of the coefficients of the three variables in three equations, then calculate $Dx$, where the x coefficients with the constant terms in the determinant $D$. Similarly calculate $Dy$ and $Dz$. Then, if $D$ is not equal to zero, the system has a unique solution. This is called consistent. If $D$ not equal to $0$, at least one of $Dx$, $Dy$, $Dz$ are not equal to zero, the system has no solution and this is called inconsistent. If $D=Dx=Dy=Dz=0$, the system has infinite solutions.
