Final answer:
The brown-eyed man with a blue-eyed mother is heterozygous with genotype Bb, and his mother is homozygous recessive with genotype bb.
Step-by-step explanation:
In humans, eye color is a result of complex inheritance patterns where multiple genes are involved. Blue eye color is recessive to brown eye color. If a brown-eyed man has a blue-eyed mother, his genotype must be heterozygous, carrying one brown (dominant) allele and one blue (recessive) allele. His mother's genotype would be homozygous recessive as blue is a recessive trait and she expresses this trait.
Using this information, we know that in the case of the brown-eyed man (Bb) and his blue-eyed mother (bb), the son has inherited a blue allele from his mother and must have inherited a brown allele from his father to exhibit the brown eye color phenotype.