Chapter 2.4, Problem 52E

BANKING The numbers of three types of bank accounts on January $1$ at the Central Bank and its branches are represented by matrix $A$:

$\begin{array}{l}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{l}\text{Checking}\\ \text{accounts}\end{array}\end{array}\begin{array}{c}\begin{array}{l}\text{Savings}\\ \text{accounts}\end{array}\end{array}\begin{array}{c}\begin{array}{l}\text{Fixed-}\\ \text{deposit}\\ \text{accounts}\end{array}\end{array}\end{array}\end{array}\\ A=\begin{array}{c}\text{Main}\text{office}\\ \text{Westside}\text{branch}\\ \text{Eastside}\text{branch}\end{array}\left[\begin{array}{c}2820\\ 1030\\ 1170\end{array}\begin{array}{c}1470\\ 520\\ 540\end{array}\begin{array}{c}1120\\ 480\\ 460\end{array}\right]\end{array}$

The number and types of accounts opened during the first quarter are represented by matrix $B$, and the number and types of accounts closed during the same period are represented by matrix $C$. Thus,

$B=\left[\begin{array}{ccc}260& 120& 110\\ 140& 60& 50\\ 120& 70& 50\end{array}\right]$ and $C=\left[\begin{array}{ccc}120& 80& 80\\ 70& 30& 40\\ 60& 20& 40\end{array}\right]$

a. Find matrix $D$, which represents the number of each type of account at the end of the first quarter at each location.

b. Because a new manufacturing plant is opening in the immediate area, it is anticipated that there will be a $10\%$ increase in the number of accounts at each location during the second quarter. Write a matrix $E=1.1D$ to reflect this anticipated increase.