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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 ______________.

  1. a unique solution for $x$
  2. infinitely many solutions for $x$
  3. no solutions for $x$
  4. exactly two solutions for $x$
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