Mathematics - Determinant Question with Solution | TestHub

Applying ${\mathrm{C}}_1-{\mathrm{C}}_2$ and ${\mathrm{C}}_2-{\mathrm{C}}_3,$ we get $\begin{array}{rl}\text{ Det. }& =\left|\begin{array}{ccc}25& 21& 219\\ 15& 27& 198\\ 21& 17& 181\end{array}\right|=\left|\begin{array}{ccc}4& 21& 9\\ -12& 27& -72\\ 4& 17& 11\end{array}\right|\\ =& [\begin{array}{llc}4& 21& 9\\ 0& 90& -45\\ 0& -4& 2\end{array}\mid \left[\mathrm{By}{\mathrm{R}}_2+3{\mathrm{R}}_1,{\mathrm{R}}_3-{\mathrm{R}}_1\right]\\ =4(180-180)=0& \end{array}$