A) 2
B) 3
C) 1
D) 0
Correct Answer: A
Solution :
Let \[A=\left[ \begin{matrix} 1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1 \\ \end{matrix} \right]\] If the matrix A is singular, then \[|A|=0\] \[\left| \begin{matrix} 1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1 \\ \end{matrix} \right|=0\] Expand with respect to \[{{R}_{1}}\] \[\Rightarrow \] \[1(x-2-1)-2(1-x)-1(1-{{x}^{2}}+2x)=0\] \[\Rightarrow \] \[x-3-2+2x-1+{{x}^{2}}-2x=0\] \[\Rightarrow \] \[{{x}^{2}}+x-6=0\] \[\Rightarrow \] \[(x-2)\,(x+3)=0\] \[\Rightarrow \] \[x=2,\,-3\]You need to login to perform this action.
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