Question
Find the value(s) of $x$, if
i) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{cc}x & 3 \\ 2 x & 5\end{array}\right|$
ii) $\left|\begin{array}{ccc}2 & 1 & x+1 \\ -1 & 3 & -4 \\ 0 & -5 & 3\end{array}\right|=0$
iii) $\left|\begin{array}{ccc}x-1 & x & x-2 \\ 0 & x-2 & x-3 \\ 0 & 0 & x-3\end{array}\right|=0$
i) $\left|\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right|=\left|\begin{array}{cc}x & 3 \\ 2 x & 5\end{array}\right|$
ii) $\left|\begin{array}{ccc}2 & 1 & x+1 \\ -1 & 3 & -4 \\ 0 & -5 & 3\end{array}\right|=0$
iii) $\left|\begin{array}{ccc}x-1 & x & x-2 \\ 0 & x-2 & x-3 \\ 0 & 0 & x-3\end{array}\right|=0$