Consider the following system of equations αx+2y+z=1 2αx+3y+z=1 3x+αy+2z=β For some α,β∈ℝ. Then which of the following is NOT correct.

Question

Consider the following system of equations

$α x + 2 y + z = 1$

$2 α x + 3 y + z = 1$

$3 x + α y + 2 z = β$

For some $α, β \in ℝ$ . Then which of the following is NOT correct.

It has no solution if

α = - 1

and

β \neq 2

It has no solution for

α = - 1

and for all

β \in ℝ

It has no solution for

α = 3

and for all

β \neq 2

It has a solution for all

α \neq - 1

and

β = 2

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