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John112
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Should the right answer to this question(below) be 14 and not 31? because
A[itex]_{ij}[/itex][itex]^{k}[/itex] means number of paths from i to j of length K. So A[itex]_{12}[/itex][itex]^{8}[/itex] = 14
We then represent the graph as indcidence matrices and go from there on:
A = { {0,1,0,0}, {1,0,1,0}, {1,1,0,1}, {1,0,0,0} }
A[itex]^{8} = { {22,14,13,4}, {31,35,14,13}, {40,31,22,10}, {10,13,4,5} }
QUESTION:
At each step the elevator is able to travel directly from floor to floor as listed below. Suppose we go floor to floor eight times (e.g 1 to 2 then 2 to 3 would be two times). How many different ways can we start at floor 1 and end at floor 2?
floor 1 to floor 2
floor 2 to floor 3
floor 3 to floor 4
floor 4 to floor 1
floor 2 to floor 1
floor 3 to floor 1
floor 3 to floor 2
Correct Answer in the back of the book: 31
A[itex]_{ij}[/itex][itex]^{k}[/itex] means number of paths from i to j of length K. So A[itex]_{12}[/itex][itex]^{8}[/itex] = 14
We then represent the graph as indcidence matrices and go from there on:
A = { {0,1,0,0}, {1,0,1,0}, {1,1,0,1}, {1,0,0,0} }
A[itex]^{8} = { {22,14,13,4}, {31,35,14,13}, {40,31,22,10}, {10,13,4,5} }
QUESTION:
At each step the elevator is able to travel directly from floor to floor as listed below. Suppose we go floor to floor eight times (e.g 1 to 2 then 2 to 3 would be two times). How many different ways can we start at floor 1 and end at floor 2?
floor 1 to floor 2
floor 2 to floor 3
floor 3 to floor 4
floor 4 to floor 1
floor 2 to floor 1
floor 3 to floor 1
floor 3 to floor 2
Correct Answer in the back of the book: 31
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