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
2
3
0
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.