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 effectively consumed by each carnivore.

(a) Find AB.

(b) What fraction of plant type 1 (row 1 of matrix A) is effectively consumed by each carnivore?

(c) Identify the plant type that each carnivore effectively consumes the most.

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Herbivores 0.2 0.1 0.4 0.3 0.3 0.1 A =| 0.2 0.1 0.1 Plants 0.1 0.2 0.5 0.4 0.4