 Hello and welcome to this session, let us understand the following problem today. Evaluate determinant 1 x y 1 x plus y y 1 x x plus y. Now let us write the solution we have delta is equal to 1 x y 1 x plus y y 1 x x plus y. Now apply r 1 tends to r 1 minus r 3 which is equal to 0 0 minus x 1 1 x plus y y x x plus y. Now expanding it through minus x so eliminating this row and this column we are left with minus x multiplied by x minus of x plus y. Now which is equal to minus x multiplied by x minus x minus y this minus x cancels with plus x so we are left with minus x minus y which is equal to plus x y. Therefore the required answer is x y. I hope you understood the problem bye and have a nice day.