Question

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

• A. 2
• B. 3
• C. 0
• D. 1

Answer 1

Answer: (D)

1

Answer 2

$\begin{vmatrix}1 & -1 & x \\\ 1 & x & 1 \\\ x & -1 & 1\end{vmatrix}$
Has no inverse;
$\Rightarrow|A|=0$
$x+1+1(1-x)+x\left(-1-x^{2}\right)=0$
$x+1+1-x-x-x^{3}=0$
$x^{3}-x-2=0$
$\Rightarrow x^{3}+2 x-x-2=0$
$\left(x^{2}-1\right)(x+2)=0$
$\Rightarrow x=\pm 1, x=-2$
Real value of $x=1$