A village is divided into three mutually exclusive groups called clans. Each person in

Chapter 2, Problem 105

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A village is divided into three mutually exclusive groups called clans. Each person in the village belongs to a clan, and this identification is permanent. There are rigid rules concerning marriage: A person from one clan can only marry a person from one other clan. These rules are encoded in the matrix A below. The fact that the 2-3 entry is 1 indicates that marriage between a man from clan III and a woman from clan II is allowed. The clan of a child is determined by the mothers clan, as indicated by the matrix B. According to this scheme siblings belong to the same clan.and likewise for the two other clans. Matrix A transforms the husbands clan into the wifes clan (if x represents the husbands clan, then Ax represents the wifes clan). a. Are the matrices A and B invertible? Find the inverses if they exist. What do your answers mean, in practical terms? b. What is the meaning of 2, in terms of the rules of the community? c. What is the meaning of AB and BA, in terms of the rules of the community? Are AB and BA the same? d. Bueya is a young woman who has many male first cousins, both on her mothers and on her fathers sides. The kinship between Bueya and each of her male cousins can be represented by one of the four diagrams below:In each of the four cases, find the matrix which gives you the cousins clan in terms of Bueyas clan. e. According to the rules of the village, could Bueya marry a first cousin? (We do not know Bueyas clan.)