In solving a system of linear equations $\mathrm{AX}=\mathrm{B}$ by Cramer's rule, in the usual notation, if $\Delta_1=\left|\begin{array}{ccc}-11 & 1 & -7 \\ -4 & 1 & -2 \\ 5 & 1 & 1\end{array}\right|$ and $\Delta_3=\left|\begin{array}{ccc}4 & 1 & -11 \\ 1 & 1 & -4 \\ 4 & 1 & 5\end{array}\right|$, then $\mathrm{X}=$

• A

  $\left[\begin{array}{c}-1 \\ 1 \\ 2\end{array}\right]$
• B

  $\left[\begin{array}{c}2 \\ 1 \\ -1\end{array}\right]$
• Correct answer
  C

  $\left[\begin{array}{c}1 \\ -1 \\ 2\end{array}\right]$
• D

  $\left[\begin{array}{c}1 \\ 2 \\ -1\end{array}\right]$

Hence, the correct answer is option: 'C'.