Sociologists often study the dominance of one group over another. Suppose in a certain society there are four classes which we will call: abigweel, aweel, upancomer, and pon. Hint: These are pronounced "A big wheel," "A wheel," "Up and comer," and "pea-on." Abigweel dominates aweel, upancomer, and pon. Aweel dominates upancomer and pon. Upancomer dominates pon.

a. Write a zero-one matrix, \([\mathrm{D}]\), representing these dominance relationships. Seebelow.

b. We say that an individual has two-stage dominance over another if 1 appears in the matrix \([D]^{2}\) for those individuals. Write the two-stage dominance matrix. Seebelow

c. We define the power of an individual as the sum of the entries in the appropriate row of the matrix

\[[\mathrm{P}]=[\mathrm{D}]+[\mathrm{D}]^{2}\]

Determine the power of abigweel, aweel, upancomer, and pon.

d. Rank the abigweel, aweel, upancomer, and pon.