A) \[\frac{13}{25}\]
B) \[-\frac{25}{13}\]
C) \[\frac{5}{13}\]
D) \[\frac{25}{13}\]
E) \[-\frac{13}{25}\]
Correct Answer: B
Solution :
\[\because \]\[\left[ \begin{matrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \\ \end{matrix} \right]\]is a singular matrix \[\therefore \] \[\left| \begin{matrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \\ \end{matrix} \right|=0\] \[\Rightarrow \]\[(2+x)(5-2)-3(-5-2x)+4(1+x)=0\] \[\Rightarrow \]\[6+3x+15+6x+4+4x=0\] \[\Rightarrow \] \[13x+25=0\] \[\Rightarrow \] \[x=-\frac{25}{13}\]
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