Consistent ?? Think again -2

Algebra Level 4

\[ \begin{cases} x_2 - 2x_3 - h = 0 \\ x_1 - x_2 + x_3 = 2 \\ x_1 = 3 - k x_2 \end{cases} \]

Given the system of equations above. What are the values of \(h\) and \(k\) so that the system is inconsistent?

A) \( k = -\dfrac12 \), \(h\subset \mathbb R -\{2 \} \).
B) \( k \subset \mathbb R - \left \{ - \dfrac12 \right\} , h = 2 \).
C) The system is always inconsistent.
D) \(k \subset \mathbb R , h \subset \mathbb R \).
E) \(k = 0\) or \(k=1\), \(h = \pm \; 2 \).

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