Consider the system of equations $$\begin{aligned}
& x - 2 y + 3 z = - 1 \\
& - x + y - 2 z = k \\
& x - 3 y + 4 z = 1 .
\end{aligned}$$ STATEMENT-1 : The system of equations has no solution for $k \neq 3$. and STATEMENT-2 : The determinant $\left| \begin{array} { c c c } 1 & 3 & - 1 \\ - 1 & - 2 & k \\ 1 & 4 & 1 \end{array} \right| \neq 0$, for $k \neq 3$. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 is True, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 is True
Consider the system of equations
$$\begin{aligned}
& x - 2 y + 3 z = - 1 \\
& - x + y - 2 z = k \\
& x - 3 y + 4 z = 1 .
\end{aligned}$$
STATEMENT-1 : The system of equations has no solution for $k \neq 3$.\\
and\\
STATEMENT-2 : The determinant $\left| \begin{array} { c c c } 1 & 3 & - 1 \\ - 1 & - 2 & k \\ 1 & 4 & 1 \end{array} \right| \neq 0$, for $k \neq 3$.\\
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1\\
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1\\
(C) STATEMENT-1 is True, STATEMENT-2 is False\\
(D) STATEMENT-1 is False, STATEMENT-2 is True