A small town has three gyms: Fit, Gymie and Hip. Each year Fit retains 70% of its members with 20% moving to Gymie and the rest to Hip. Gymie retains 60%, losing the rest in equal numbers to its rivals. Hip

retains just 30% with 40% moving to Fit and 30% moving to Gymie. There are no other changes to the gym membership in the town.

(a) If x= [1000, 800, 800] is a 3 x 1 matrix for the current numbers, show that it is possible to

work out next year's membership figures by performing a matrix multiplication Ax, where

A is a 3 x 3 matrix which should be stated.

(b) Use matrix multiplication to work out the number of members in Fit 2 years from now.

(a) A =