Consider a system of linear equations $Ax = b,$ where
$A =\begin{bmatrix} 1 & – \sqrt{2} & 3 \\ – 1 & \sqrt{2} & – 3 \end{bmatrix}, \quad b = \begin{bmatrix} 1 \\ 3 \end{bmatrix}.$
This system of equations admits ______________.
- a unique solution for $x$
- infinitely many solutions for $x$
- no solutions for $x$
- exactly two solutions for $x$