A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another.        Elec.  Gas    Oil    Solar   Electricity Natural Gas Fuel Oil Solar Energy 0.60 0.05 0.10 0 0.15 0.85 0.10 0.07 0.10 0.02 0.75 0.07 0.15 0.08 0.05 0.86 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, what percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.5: Markov Chain
Problem 47E: Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.
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A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another.
       Elec.  Gas    Oil    Solar
  Electricity

Natural Gas

Fuel Oil

Solar Energy
0.60
0.05 0.10 0
0.15 0.85 0.10 0.07
0.10 0.02 0.75 0.07
0.15 0.08 0.05 0.86
Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, what percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.)
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