Question

The system of linear equations in x1, x2, x3
$\begin{pmatrix} 1 & 1 & 1 \\\ 0 & -1 & 1 \\\ 2 & 3 & \alpha \end{pmatrix}\begin{pmatrix} x_1 \\\ x_2 \\\ x_3 \end{pmatrix}=\begin{pmatrix} 3 \\\ 1 \\\ \beta \end{pmatrix}$
where α, β ∈ R, has

• A. at least one solution for any α and β
• B. a unique solution for any β when α ≠ 1
• C. NO solution for any α when β ≠ 5
• D. infinitely many solutions for any α when β = 5

Answer 1

Answer: (B)

a unique solution for any β when α ≠ 1

Answer 2

The correct option is (B) : a unique solution for any β when α ≠ 1.