Question

If $\left[\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right]$ has no inverse, then the real value of $x$ is

• A. $2$
• B. $3$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

$A=\left|\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right|hasnoinversex$

$if\left|A\right|=0$

$\left|\begin{array}{ccc}1& -1& x\\ 1& x& 1\\ x& -1& 1\end{array}\right|=0$

$1\left(x+1\right)-1\left(-1+x\right)+x\left(-1-x^2\right)=0$

$x+1+1-x-x-x^3=0$

$-x^3-x+2=0$

$x^3+x-2=0$

$\left(x-1\right)\left(x^2+x+2\right)=0$

$x=1isrealvalue$