Consider the following system of questions $$\begin{aligned}
& \alpha x + 2 y + z = 1 \\
& 2 \alpha x + 3 y + z = 1 \\
& 3 x + \alpha y + 2 z = \beta
\end{aligned}$$ For some $\alpha , \beta \in \mathbb { R }$. Then which of the following is NOT correct. (1) It has no solution if $\alpha = - 1$ and $\beta \neq 2$ (2) It has no solution for $\alpha = - 1$ and for all $\beta \in \mathbb { R }$ (3) It has no solution for $\alpha = 3$ and for all $\beta \neq 2$ (4) It has a solution for all $\alpha \neq - 1$ and $\beta = 2$
Consider the following system of questions
$$\begin{aligned}
& \alpha x + 2 y + z = 1 \\
& 2 \alpha x + 3 y + z = 1 \\
& 3 x + \alpha y + 2 z = \beta
\end{aligned}$$
For some $\alpha , \beta \in \mathbb { R }$. Then which of the following is NOT correct.\\
(1) It has no solution if $\alpha = - 1$ and $\beta \neq 2$\\
(2) It has no solution for $\alpha = - 1$ and for all $\beta \in \mathbb { R }$\\
(3) It has no solution for $\alpha = 3$ and for all $\beta \neq 2$\\
(4) It has a solution for all $\alpha \neq - 1$ and $\beta = 2$