🛠️ JEE➗ Maths

Consider the following system of equations \( \begin{aligned} & \alpha x+2 y+z=1 \\ & 2 \alpha x+3 y+z=1 \\ &amp…

Q1

Consider the following system of equations
\(
\begin{aligned}
& \alpha x+2 y+z=1 \\
& 2 \alpha x+3 y+z=1 \\
& 3 x+\alpha y+2 z=\beta
\end{aligned}
\)

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

[JEE Main 2023, 29 Jan (Shift 1)]

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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