The system of linear equations in x1, x2, x3
\(\left(\begin{array}{ccc} 1 & 1 & 1 \\ 0 & -1 & 1 \\ 2 & 3 & \alpha \end{array}\right)\left(\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right)=\left(\begin{array}{l} 3 \\ 1 \\ \beta \end{array}\right)\)
where α, β ∈ ℝ, has
1
at least one solution for any α and β
2
a unique solution for any β when α ≠ 1
3
NO solution for any α when β ≠ 5
4
infinitely many solutions for any α when β = 5