Answer
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 $B-A=\left[ \begin{matrix}
7 & 23 \\
34 & 31 \\
\end{matrix} \right]$.
Work Step by Step
(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.
