Suppose that at a pixel $(x,y)$ on a color monitor we would like to generate a spectral power distribution $I().$ We are given the spectral power distributions $D_R(),D_G(),D_B()$ for the three display guns.

a$)$ Is it possible, in general, to find constants $r,g,b$ such that $I()=r{D}_R()+g{D}_G()+b{D}_B().$ Explain your answer.

b$)$ Given $I(),$ find constants $r,g,b$ such that $r{D}_R()+g{D}_G()+b{D}_B()$ looks the same as $I()$ to a standard human observer. Explain all symbols in your equations.

c$)$ Suppose that the display guns are related by $D_G()=3D_R()+2D_B().$ How will this relationship affect the computation of the $r,g,b$ values in part $b?$ Be specific.