Mathematics - Matrices Question with Solution | TestHub

$\begin{array}{rl}\text{ Let }A& =\left[\begin{array}{lll}{a}_1& a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3\end{array}\right]\\ A\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right]& =3\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right]\end{array}$ $\Rightarrow a_1+a_2+a_3=3$ ...(1) $\Rightarrow b_1+b_2+b_3=3$ ...(2) $\Rightarrow c_1+{\mathrm{ca}}_2+{\mathrm{c}}_3=3$ ...(3) Now, $\begin{array}{rl}& |A|=\left(a_1{b}_2{c}_3+a_2{b}_3{c}_1+a_3{b}_1{c}_2\right)\\ & -\left(a_3{b}_2{c}_1+a_2{b}_1{c}_3+a_1{b}_3{c}_2\right)\end{array}$ $\therefore$ From above in formation, clearly $|\mathrm{A}{|}_{\max }=27$, when $a_1=3,b_2=3,c_3=3$