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

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

$A^{-1}=\underset{|A|}{adjA}$

when $|A|=0A^{-1}$ doesn't exist.

Det $A=1\left(x\right(1)-(-1\left)\right(1\left)\right)-(-1)\left[1\right(1)-(x\left)\right(1\left)\right]+x[-1-x^2]$

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

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

$2-x-x^3=0$

$x^3+x-2=0$ when $x=1$