Set up the system of equations and then solve it by using inverse matrices.
Bee ancestry Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number of ancestors of a male t + 2 bee generations before the present generation is the sum of the number of ancestors t and t + 1 generations before the present. If the numbers of ancestors of a male bee in a given generation t and in the previous generation are given by , then there is a matrix M such that the numbers of ancestors in the two generations preceding generation t are given by .

For a given male bee, the numbers of ancestors 5 and 6 generations back are given by .

Find the numbers of ancestors 4 and 5 generations back by multiplying both sides of by the inverse of M.

Question

Set up the system of equations and then solve it by using inverse matrices. ​
Bee ancestry Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number  of ancestors of a male t + 2 bee generations before the present generation is the sum of the number of ancestors t and t + 1 generations  before the present. If the numbers of ancestors of a male bee in a given generation t and in the previous generation are given by  , then there is a matrix M such that the numbers of ancestors in the two generations preceding generation t are given by  .
​
For a given male bee, the numbers of ancestors 5 and 6 generations back are given by  .
​
Find the numbers of ancestors 4 and 5 generations back by multiplying both sides of  by the inverse of M.
​

Quizplus · Accepted Answer

The Answer of Set up the system of equations and then solve it by using inverse matrices. ​
Bee ancestry Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number  of ancestors of a male t + 2 bee generations before the present generation is the sum of the number of ancestors t and t + 1 generations  before the present. If the numbers of ancestors of a male bee in a given generation t and in the previous generation are given by  , then there is a matrix M such that the numbers of ancestors in the two generations preceding generation t are given by  .
​
For a given male bee, the numbers of ancestors 5 and 6 generations back are given by  .
​
Find the numbers of ancestors 4 and 5 generations back by multiplying both sides of  by the inverse of M.
​

Set Up the System of Equations and Then Solve It