The system of linear equations |
\[x+y+z=2\] |
\[2x+3y+2z=\text{ }5\] |
\[2x+3y+\left( {{a}^{2}}-1 \right)z\text{ }=\text{ }a+1\] |
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 \[\left| a \right|\,\,=\,\,\sqrt{3}\]You need to login to perform this action.
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