Mathematics - Determinant Question with Solution | TestHub

Let $\left|\begin{array}{ccc}(1+x{)}^{a_2{b}_1}& (1+x{)}^{a_1{b}_2}& (1+x{)}^{a_1{b}_2}\\ (1+x{)}^{a_2{b}_1}& (1+x{)}^{a_2{b}_2}& (1+x{)}^{a_2{b}_2}\\ (1+x{)}^{a_2{b}_2}& (1+x{)}^{a_2{b}_2}& (1+x{)}^{a_2{b}_2}\end{array}\right|={\lambda }_0+{\lambda }_{1}x+{\lambda }_2{x}^2+{\lambda }_3{x}^3+\dots$. For ${\lambda }_1$, differentiate with respect to $x$ and set $x=0$.