If GENETIC STOCKS AND BREEDING METHODS 



Solving the determinant, 



|1 - A1K1/4) - X][X 2 - (1/2)X - (1/4)1 = 0, 



yielding the roots 



Xx = (1 + V5)/4, 



X 2 = (1 - V5)/4, 



X 3 = 1/4, 

 and 



X 4 = 1. 



These are the roots found by solving the three linear equations for a proportionality 

 constant, with the addition of the root X 4 = 1 . From these the A matrix given in 

 table 5 (a) is derived. Substituting the above values of X* into formula (7), the matrix 

 A, given in table 5 (b) and its inverse, A -1 , table 5 (c) are obtained. 



Table 5 

 The matrices A, A, and A -1 for brother-sister mating 



(a) A = 



(b) A = 



(c) A' 1 = 



Now, 



if all matings in the initial generation are assumed to be cross mat'^gs. Then 



