Consider the following system of questions $\alpha x+2 y+z=1$ ; $2 \alpha x+3 y+z=1$ ; $3 x+\alpha y+2 z=\beta$ . For some $\alpha, \beta \in R$. Then which of the following is NOT correct.
Consider the following system of questions $\alpha x+2 y+z=1$ ; $2 \alpha x+3 y+z=1$ ; $3 x+\alpha y+2 z=\beta$ . For some $\alpha, \beta \in R$. Then which of the following is NOT correct.
- [JEE MAIN 2023]
- A
It has no solution if $\alpha=-1$ and $\beta \neq 2$
- B
It has no solution for $\alpha=-1$ and for all $\beta \in R$
- C
It has no solution for $\alpha=3$ and for all $\beta \neq 2$
- D
It has a solution for all $\alpha \neq-1$ and $\beta=2$
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