Table 5. The inverse of the genetic-effect design matrix shown in Table 4.

	Genotypic values
Genetic effects	M11O11	M11O21	M12O11	M12O21	M12O12	M12O22	M22O12	M22O22
R	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{8}$
ao	0	0	$\frac{1}{2}$	0	0	−$\frac{1}{2}$	0	0
do	−$\frac{1}{4}$	$\frac{1}{4}$	−$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$	−$\frac{1}{4}$	$\frac{1}{4}$	−$\frac{1}{4}$
io	0	0	0	−$\frac{1}{2}$	$\frac{1}{2}$	0	0	0
am	0	$\frac{1}{2}$	0	0	0	0	−$\frac{1}{2}$	0
dm	−$\frac{1}{4}$	−$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{4}$	−$\frac{1}{4}$	−$\frac{1}{4}$
cmo	$\frac{1}{2}$	0	0	0	0	0	0	−$\frac{1}{2}$
ddmo	$\frac{1}{2}$	−$\frac{1}{2}$	−$\frac{1}{2}$	$\frac{1}{2}$	$\frac{1}{2}$	−$\frac{1}{2}$	−$\frac{1}{2}$	$\frac{1}{2}$

The inverse of the genetic-effect design matrix in Table 4 gives the solution to the vector of genetic effects from the linear model. The columns of the matrix are labeled with the genotypic effect and the rows are labeled with the corresponding genetic effect.