Matrices And Determinants

Consider the system of equations:

\(x-2y+3z=-1\)

\(-x+y-2z=k\)

\(x-3y+4z=1\)

Statement - 1 : The system of equations has no solution for \(k\ne3\).

and

Statement - 2 : The determinant \(\left| {\matrix{ 1 & 3 & { - 1} \cr { - 1} & { - 2} & k \cr 1 & 4 & 1 \cr } } \right| \ne 0\), for \(k \ne 3\).