Answer
a. $\begin{bmatrix} 15,800 & 18,600 \\ 12,500 & 14,800 \\ 3700 & 4600 \end{bmatrix}$
b. $14,800$
c. $15,800$
Work Step by Step
a. Using the given matrices, we have
$AB=\begin{bmatrix} 0.4 & 0.3 & 0.7 \\ 0.3 & 0.6 & 0.25 \\ 0.3 & 0.1 & 0.05 \end{bmatrix} \begin{bmatrix} 6000 & 8000 \\ 12,000 & 14,000 \\ 14,000 & 16,000 \end{bmatrix}=
\begin{bmatrix} 15,800 & 18,600 \\ 12,500 & 14,800 \\ 3700 & 4600 \end{bmatrix}$
b. Female is column-2 and Democrat is row-2. Thus, there are $14,800$ female Democrats.
c. Male is column-1 and Republican is row-1. Thus, there are $15,800$ male Republicans.
