question_answer

The system of linear equations

\[x+y+z=2\]

\[2x+3y+2z=\text{ }5\]

\[2x+3y+\left( {{a}^{2}}-1 \right)z\text{ }=\text{ }a+1\]

[JEE Main Online Paper (Held On 09-Jan-2019 Morning]

A) has infinitely many solutions for \[a=4\]

B) has a unique solution for I a I \[=\,\,\sqrt{3}\]

C) is inconsistent when I a I = \[=\,\,\sqrt{3}\]

D) is inconsistent when \[a=4\]

Correct Answer: C

Solution :

\[=\text{ }3\left( {{a}^{2}}-1 \right)-6-2\left( {{a}^{2}}-1 \right)+4\,\,\,+\,\,0\,\,={{a}^{2}}\,\,-\,\,3\] For unique solution \[\Delta \,\,\ne \,\,0\] \[a\,\,\ne \,\,\pm \,\,\sqrt{3}\] \[\therefore \] For inconsistent \[\left| a \right|\,\,=\,\,\sqrt{3}\]