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(4) Three firms, F₁, F2, F3 share the market for a certain commodity. F₁ has 20%, F₂ has 60% and F3 has 20%. In the following year the changes accour: F₁ keeps 85% of its consumers, loses 5% to F2 and 10% to F3 F2 keeps 55% of its consumers, loses 10% to F₁ and 35% to F3 F3 keeps 85% of its consumers, loses 10% to F₁ and 5% to F₂. Write the matrix S = the initial share and the matrix T = tij, the transformation matrix, where tij = what F; gets from F;. Compute TS, T· (T-S), T (T- (TS)). What do they represent?

(4) Three firms, F₁, F2, F3 share the market for a certain commodity. F₁ has 20%, F₂ has 60% and F3 has 20%. In the following year the changes accour: F₁ keeps 85% of its consumers, loses 5% to F2 and 10% to F3 F2 keeps 55% of its consumers, loses 10% to F₁ and 35% to F3 F3 keeps 85% of its consumers, loses 10% to F₁ and 5% to F₂. Write the matrix S = the initial share and the matrix T = tij, the transformation matrix, where tij = what F; gets from F;. Compute TS, T· (T-S), T (T- (TS)). What do they represent?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(4) Three firms, F₁, F2, F3 share the market for a certain commodity. F₁ has 20%, F2 has 60% and F3 has 20%. In the following year the changes accour: F₁ keeps 85% of its consumers, loses 5% to F2 and 10% to F3 F2 keeps 55% of its consumers, loses 10% to F₁ and 35% to F3 F3 keeps 85% of its consumers, loses 10% to F₁ and 5% to F2. Write the matrix S = the initial share and the matrix T = tij, the transformation matrix, where tij = what F; gets from Fj. Compute T - S,T· (TS), T · (T · (T· S)). What do they represent? (5) Calculate the following determinants: 3 -1 2 0 −1 -1 6 1 2 2-0 3 -1 0 4 0 0 0 1 -1 2 3 2 5 -3 30 1 1 0 -1 20 5
Transcribed Image Text:(4) Three firms, F₁, F2, F3 share the market for a certain commodity. F₁ has 20%, F2 has 60% and F3 has 20%. In the following year the changes accour: F₁ keeps 85% of its consumers, loses 5% to F2 and 10% to F3 F2 keeps 55% of its consumers, loses 10% to F₁ and 35% to F3 F3 keeps 85% of its consumers, loses 10% to F₁ and 5% to F2. Write the matrix S = the initial share and the matrix T = tij, the transformation matrix, where tij = what F; gets from Fj. Compute T - S,T· (TS), T · (T · (T· S)). What do they represent? (5) Calculate the following determinants: 3 -1 2 0 −1 -1 6 1 2 2-0 3 -1 0 4 0 0 0 1 -1 2 3 2 5 -3 30 1 1 0 -1 20 5
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