## Precalculus (6th Edition) Blitzer

a) The data for the year 2000 can be represented by the matrix $A=\left[ \begin{matrix} 2 & 6 \\ 31 & 46 \\ \end{matrix} \right]$. b) The data for the year 1960 can be represented by the matrix $B=\left[ \begin{matrix} 9 & 29 \\ 65 & 77 \\ \end{matrix} \right]$. c) The difference between the matrices B and A is $B-A=\left[ \begin{matrix} 7 & 23 \\ 34 & 31 \\ \end{matrix} \right]$.
(a) The above data can be represented in the form of a matrix as below: $A=\left[ \begin{matrix} 2 & 6 \\ 31 & 46 \\ \end{matrix} \right]$ Therefore, the matrix is $\left[ \begin{matrix} 2 & 6 \\ 31 & 46 \\ \end{matrix} \right]$. (b) The above data can be represented in the form of a matrix as below: $B=\left[ \begin{matrix} 9 & 29 \\ 65 & 77 \\ \end{matrix} \right]$ Therefore, the matrix is $\left[ \begin{matrix} 9 & 29 \\ 65 & 77 \\ \end{matrix} \right]$. (c) This represents the difference between the percentages of people completing the transition to adulthood in $1960$ and $2000$ by age and gender. The difference of matrices A and B is as below: \begin{align} & B-A=\left[ \begin{matrix} 9 & 29 \\ 65 & 77 \\ \end{matrix} \right]-\left[ \begin{matrix} 2 & 6 \\ 31 & 46 \\ \end{matrix} \right] \\ & =\left[ \begin{matrix} 7 & 23 \\ 34 & 31 \\ \end{matrix} \right] \end{align} Therefore, the matrix is $\left[ \begin{matrix} 7 & 23 \\ 34 & 31 \\ \end{matrix} \right]$. It is the difference between the percentages of people completing the transition to adulthood in $1960$ and $2000$ by age and gender.