Under which of the following condition$(s)$ does the system of equations $\begin{bmatrix} 1 & 2 & 4 \\ 2 & 1 & 2 \\ 1 & 2 & a-4 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ a \end{bmatrix}$ possess a unique solution?

  • A
    $\forall a \in \mathbb{R}$
  • B
    $a = 8$
  • C
    for all integral values of $a$
  • D
    $a \neq 8$

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