Q77 / 180 · KCET 2011 · Mathematics

If $\left[\begin{array}{ccr}1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1\end{array}\right]$ is singular, then the value of $x$ is

  • Correct answer
    A
    2
  • B
    3
  • C
    1
  • D
    0

Solution

Let $A=\left[\begin{array}{ccc}1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1\end{array}\right]$ if the matrix $A$ is singular, then $|A|=0$ $$ \left|\begin{array}{ccc} 1 & 2 & -1 \\ 1 & x-2 & 1 \\ x & 1 & 1 \end{array}\right|=0 $$ Expand with respect to $R_{1}$ $\Rightarrow 1(x-2-1)-2(1-x)-1\left(1-x^{2}+2 x\right)=0$ $\Rightarrow \quad x-3-2+2 x-1+x^{2}-2 x=0$ $\Rightarrow \quad x^{2}+x-6=0$ $\Rightarrow \quad(x-2)(x+3)=0$ $\Rightarrow \quad x=2,-3$

Hence, the correct answer is option: 'A'.

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