If $\left[\begin{array}{rrr}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse, then…

If $\left[\begin{array}{rrr}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{array}\right]$ has no inverse, then the real value of $x$ is
  1. 2
  2. 3
  3. 0
  4. 1

Solution

If matrix has no inverse it means the value of determinant should be zero. $\therefore \quad\left|\begin{array}{rrr} 1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1 \end{array}\right|=0$ If we put $x=1$, then column Ist and IIIrd are identical. Hence, option (d) is correct.

Asked in: AP EAMCET 2009

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