The system of linear equations.
$x+y+z=2$
$2 x+3 y+2 z=5$
$2 x+3 y+\left(a^{2}-1\right) z=a+1$
Correct Option: , 2
$\mathrm{D}=\left|\begin{array}{ccc}1 & 1 & 1 \\ 2 & 3 & 2 \\ 2 & 3 & \mathrm{a}^{2}-1\end{array}\right|=\mathrm{a}^{2}-3$
$D_{1}=\left|\begin{array}{ccc}2 & 1 & 1 \\ 5 & 3 & 2 \\ a+1 & 3 & a^{2}-1\end{array}\right|=a^{2}-a+1$
$\mathrm{D}_{2}=\left|\begin{array}{ccc}1 & 2 & 1 \\ 2 & 5 & 2 \\ 2 & a+1 & a^{2}-1\end{array}\right|=a^{2}-3$
$\mathrm{D}_{3}=\left|\begin{array}{ccc}1 & 1 & 2 \\ 2 & 3 & 5 \\ 2 & 3 & \mathrm{a}+1\end{array}\right|=\mathrm{a}-4$
$\mathrm{D}=0$ at $|\mathrm{a}|=\sqrt{3}$ but $\mathrm{D}_{3}=\pm \sqrt{3}-4 \neq 0$
So the system is Inconsistant for $|\mathrm{a}|=\sqrt{3}$
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