1. (30) Our new experimental reactor emits all neutrons at 2MeV. To best analyze the neutron population, we will consider a 3 -group diffusion equation. Group 1 is above 1MeV, Group 2 is from 1eV to 1MeV, and Group 3 is from 0eV to 1eV. Do not consider up-scattering in energy (a) Write out all of the losses and gains in each energy group in words and in equation form. (b) Write the diffusion equation for each group. (c) Translate the diffusion equations to matrix form. (d) To find the non-trivial solution, the determinant of the matrix must be zero. Set up the equations to solve for the determinant of the matrix