Expressing the given vectors using matrix multiplication:

Suppose $Ct$ be the number of children in Indiana at the beginning of the year $t$ and $At$ be the number of adults in Indiana at the beginning of year $t$ .

Since during any year $t$ , 5% of all the children become adults and 1% of all children die, the number of children at the beginning of the year $t+1$ is 96% of the previous year.

Hence, the number of children in the beginning of the year $t+1$ is,

$Ct+1=0.96Ct$

Also, during any year $t$ , 3% of all adults die. So, 97% of all adults will live in the beginning of the year $t+1$ .

Therefore, the number of adults in the beginning of the year $t+1$ is,

$At+1=0$

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Chapter 2 Solutions

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Solution Summary: The author explains the relation between matrices using matrix multiplication. Suppose C_t be the number of children in Indiana at the beginning of the year T and A

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Chapter 2 Solutions