Chapter 2.5, Problem 46E

INVESTMENTS Megan manages three portfolios, $\text{I}$, $\text{II}$ and $\text{III}$ for three investors. The number of shares of four stocks $-$ FB, GE, IBM and BAC $-$ in each account given by a matrix,

$\begin{array}{l}\text{I}\text{II}\text{III}\\ B=\begin{array}{c}\text{FB}\\ \text{GE}\\ \begin{array}{l}\text{IBM}\\ \text{BAC}\end{array}\end{array}\left[\begin{array}{ccc}500& 1000& 600\\ 1000& 400& 700\\ \begin{array}{l}400\\ 3000\end{array}& \begin{array}{l}1000\\ 800\end{array}& \begin{array}{l}600\\ 1000\end{array}\end{array}\right]\end{array}$

The closing price of FB, GE, IBM and BAC on a certain day were $\$114.16$, $\$30.55$, $\$148.46$ and $\$13.19$ per share respectively.

a. Write a $4\times 4$ diagonal matrix $A$ with $a_{11}=114.16$, $a_{22}=30.55$, $a_{33}=148.46$, and $a_{44}=13.19$ find $AB$ and give an interpretation for the entries.

b. Find the sum of entries in each column of $AB$. What does each some represent?