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  4. If [1 -1 x 1 x 1 x -1 1] has no inverse, then the real value of x is

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Q. If $\begin{bmatrix}1 & -1 & x \\ 1 & x & 1 \\ x & -1 & 1\end{bmatrix}$ has no inverse, then the real value of $x$ is

EAMCETEAMCET 2009

Solution:

If matrix has no inverse it meams the value of determinant should be zero.
$\therefore \begin{vmatrix}1 & -1 & x \\1 & x & 1 \\x & -1 & 1\end{vmatrix}=0$
If we put $x=1$, then column Ist and IIIrd are identical.