In an ecological model, matrix A gives the fractions of several types of plants consumed by the herbivores in the ecosystem. Similarly, matrix B gives the fraction of each type of herbivore that is consumed by the carnivores in the system. Each row of matrix A refers to a type of plant, and each column refers to a kind of herbivore. Similarly, each row of matrix B is a kind of herbivore and each column is a kind of carnivore. The matrix AB gives the fraction of each plant that is consumed by each carnivore. (a) Find AB. (b) What fraction of plant type 1 (row 1) is consumed by each carnivore? (c) Identify the plant type that each carnivore consumes the most.
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