Answer
$a.\quad=\left[\begin{array}{l}
5\\
22\\
7
\end{array}\right]$
$b.$
5 members have no postsecondary education,
22 have 1 to 4 years postsecondary education, and
7 have more than 4 years postsecondary education
Work Step by Step
$a.$
$AB=\left[\begin{array}{lll}
0.75 & 0.1 & 0\\
0.25 & 0.7 & 0.7\\
0 & 0.2 & 0.3
\end{array}\right]\left[\begin{array}{l}
4\\
20\\
10
\end{array}\right]=\left[\begin{array}{l}
0.75(4)+0.1(20)+0(10)\\
0.25(4)+0.7(20)+0.7(10)\\
0 (4)+0.2(20)+0.3(10)
\end{array}\right]$
$=\left[\begin{array}{l}
5\\
22\\
7
\end{array}\right]$
$b.$
The rows of AB retain the row labels of A. So,
5 members have no postsecondary education,
22 have 1 to 4 years postsecondary education, and
7 have more than 4 years postsecondary education
