Simplify[
      Solve[{(1 + ϵ)*(δ^β) - ϵ == 
            α*δ, 
          β*(1 + ϵ)*(δ^(β - 1)) == 
            α}, {α, ϵ}]]

\(rgb2xyz[c_] := 
      Block[{f, s}, 
		
        f := {{c[\([1, 1]\)]/c[\([1, 2]\)], c[\([2, 1]\)]/c[\([2, 2]\)], 
              c[\([3, 1]\)]/c[\([3, 2]\)]}, {1, 1, 1}, {
              \((1 - c[\([1, 1]\)] - c[\([1, 2]\)])\)/c[\([1, 2]\)], 
              \((1 - c[\([2, 1]\)] - c[\([2, 2]\)])\)/c[\([2, 2]\)], 
              \((1 - c[\([3, 1]\)] - c[\([3, 2]\)])\)/c[\([3, 2]\)]}}; 
		
        s := Inverse[
              f].{{c[\([4, 1]\)]/c[\([4, 2]\)]}, {1}, {
                \((1 - c[\([4, 1]\)] - c[\([4, 2]\)])\)/c[\([4, 2]\)]}}; 

        		{{f[\([1, 1]\)]*s[\([1, 1]\)], f[\([1, 2]\)]*s[\([2, 1]\)], 
            f[\([1, 3]\)]*s[\([3, 1]\)]}, {f[\([2, 1]\)]*s[\([1, 1]\)], 
            f[\([2, 2]\)]*s[\([2, 1]\)], f[\([2, 3]\)]*s[\([3, 1]\)]}, {
            f[\([3, 1]\)]*s[\([1, 1]\)], f[\([3, 2]\)]*s[\([2, 1]\)], 
            f[\([3, 3]\)]*s[\([3, 1]\)]}}]\)

rgb2xyz470m := 
      rgb2xyz[{{0.67, 0.33}, {0.21, 0.71}, {0.14, 0.08}, {0.31006, 0.31616}}]

rgb2xyz470bg := 
      rgb2xyz[{{0.64, 0.33}, {0.29, 0.60}, {0.15, 0.06}, {0.312713, 
            0.329016}}]

Inverse[rgb2xyz470m].rgb2xyz470bg

{{0.698396023265322796`, 0.238769879837914045`, 
        0.0319418141018277257`}, {0.0193016340794852858`, 
        1.07270629882618173`, -0.0595741939777363604`}, {
        0.0169397711000759425`, 0.0525463647870810568`, 
        0.844972920358327428`}}

Inverse[rgb2xyz470bg].rgb2xyz470m

{{1.44248717582308438`, -0.317311108580498713`, 
        -0.0769009386960246565`}, {-0.0274664218099758317`, 
        0.93505506441107542`, 0.0669636597378669851`}, {
        -0.0272105074605999508`, -0.051786945959321704`, 
        1.18084729506325203`}}

yuv2rgb[kb_, kr_]
         := {{1, 0, 2*(1 - kr)}, {1, 
          2*((kb - 1)*kb/(1 - kb - kr)), 
          2*((kr - 1)*kr/(1 - kb - kr))}, {1, 2*(1 - kb), 0}}

yuv2rgb[0.114, 0.299] // MatrixForm

rgb2yuv[kb_, kr_]
         := {{kr, (1 - kr - kb), kb}, {
          (1/2)*(-kr)/(1 - kb), 
          (1/2)*(kr + kb - 1)/(1 - kb), 
          (1/2)*(1 - kb)/(1 - kb)}, {
          (1/2)*(1 - kr)/(1 - kr), 
          (1/2)*(kr + kb - 1)/(1 - kr), 
          (1/2)*(-kb)/(1 - kr)}}

rgb2yuv[0.114, 0.299] // MatrixForm