# Chapter 8 - Section 8.3 - Matrix Operations and Their Applications - Exercise Set - Page 919: 64

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.

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