Chapter 2.3, Problem 52E

a.

To determine

To find: the row matrix to represent Mrs. Numkena’s portfolio.

Answer to Problem 52E

  $$

  $\left[\begin{array}{cccc}42& 59& 21& 18\end{array}\right]$

Explanation of Solution

Given information: The given matrix equation is as follows:

  $\begin{array}{cc}& \begin{array}{ccc}\text{July}& \text{August}& \text{Septmeber}\end{array}\\ \begin{array}{c}\text{Stock A}\\ \text{Stock B}\\ \text{Stock C}\\ \text{Stock D}\end{array}& \left[\begin{array}{ccc}\begin{array}{l}\$33.81\\ \$15.06\\ \$54\\ \$52.06\end{array}& \begin{array}{l}\$30.94\\ \$13.25\\ \$54\\ \$44.69\end{array}& \begin{array}{l}\$27.25\\ \$8.75\\ \$46.44\\ \$34.38\end{array}\end{array}\right]\end{array}$

Mrs. Numkena’s share in each stock is as follows:

Stock A= 42 shares

Stock B= 59 shares

Stock C= 21 shares

Stock D= 18 shares

Calculation:

The row matrix representing the portfolio of Mrs. Numkena is as follows:

  $\left[\begin{array}{cccc}42& 59& 21& 18\end{array}\right]$

Here, the row represents the share and column represents the stocks.

b.

To determine

To find: the total value of Mrs. Numkena’s portfolio for each month to the nearest cent by using multiplication matrix.

Answer to Problem 52E

  $\left[\begin{array}{ccc}\$4379.64& \$4019.65& \$3254.83\end{array}\right]$

Explanation of Solution

Given information: The given matrix equation is as follows:

  $\begin{array}{cc}& \begin{array}{ccc}\text{July}& \text{August}& \text{Septmeber}\end{array}\\ \begin{array}{c}\text{Stock A}\\ \text{Stock B}\\ \text{Stock C}\\ \text{Stock D}\end{array}& \left[\begin{array}{ccc}\begin{array}{l}\$33.81\\ \$15.06\\ \$54\\ \$52.06\end{array}& \begin{array}{l}\$30.94\\ \$13.25\\ \$54\\ \$44.69\end{array}& \begin{array}{l}\$27.25\\ \$8.75\\ \$46.44\\ \$34.38\end{array}\end{array}\right]\end{array}$

The row matrix representing the portfolio of Mrs. Numkena is as follows:

  $\left[\begin{array}{cccc}42& 59& 21& 18\end{array}\right]$

Here, the row represents the share and column represents the stocks.

Calculation:

The total value of Mrs. Numkena’s portfolio for each month can be evaluated as follows:

  $\begin{array}{c}\text{Total value}=\left[\begin{array}{cccc}42& 59& 21& 18\end{array}\right]\cdot \left[\begin{array}{ccc}\begin{array}{l}\$33.81\\ \$15.06\\ \$54\\ \$52.06\end{array}& \begin{array}{l}\$30.94\\ \$13.25\\ \$54\\ \$44.69\end{array}& \begin{array}{l}\$27.25\\ \$8.75\\ \$46.44\\ \$34.38\end{array}\end{array}\right]\\ =\left[\begin{array}{ccc}\$4379.64& \$4019.65& \$3254.83\end{array}\right]\end{array}$

Thus the total value of Mrs. Numkena’s portfolio for July, August and September is $\$4379.64,$

  $\text{\$}4019.65\text{,}$ and $\$3254.83$ respectively.