Question

Write the element $a_{12}$ of the matrix $A={\left[a_{ij}\right]}_{2\times 2}$, whose elements $a_{ij}$ are given by $a_{ij}=e^{2ix}\sin jx$.

Answer 1

Given, $A={\left[a_{ij}\right]}_{2\times 2}$, where $a_{ij}=e^{2ix}\sin jx$

$\therefore a_{12}=e^{2\times 1\times x}\sin (2\times x)=e^{2x}\sin 2x$