Linear Algebra -Change of Bases and Markov Chains.

  

Week 5 Linear Algebra.docx
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Week 5
1. ?h?? ?h?? ? = {1 – ? + ? 2 , 1 + ? – 2? 2 , 3 + ? – ? 2 + ? 3 , 4 + ? 3 } Cannot be a basis of ?3 (x)
2. For the polynomial ?(?) = 2 – ? + ? 2 + 4? 3 ? ?3 ,
????? ?h? ??????????? ?? ?(?) ?? ?h? ???????? ????? {1, ?, ? 2 , ? 3 }.
3. Write the change of coordinate matrix from B to C and from C to B
1 1 2
1
1
-1
Where B = {[2] , [1] , [1]} ??? ? = {[ 1 ] , [-1] , [ 1 ]} are two basis of ? 3
1 1 1
-1
1
1
4. In a certain country, every year 15% of the residents from the big cities
move to suburbs, 3% move to rural area, rest stay in the big cities.
10% of the residents in the suburbs move to the big cities, 6% move to the
rural areas, rest stay in the suburbs.
15% of the people in the rural areas move to big cities, 30% move to the
suburbs, and the rest stay in the rural areas.
If the same transition pattern continues, find the % of the population that
will live in big cities, suburbs, and the rural areas in the long run.

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