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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…

Q1
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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 \(\alpha, \beta \in R\). Then which of the following is NOT correct.

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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