Chapter 8.2, Problem 80E

a.

To determine

To organize: the times spent exercising in a matrix B .

Answer to Problem 80E

  $B=\left[\begin{array}{ccc}2& 0.25& 0.5\end{array}\right]$

Explanation of Solution

Given:

A 130-pound person and a 155-pound person play basketball for 2 hours, jump rope for 15 minutes, and lift weights for 30 minutes.

Consider,

Time spent playing basketball = 2 hours

Time spent on jump rope = 15 minutes = 0.25 hour

Time spent in lifting weights = 30 minutes = 0.5 hour

This data can be organized in matrix form as:

  $B=\left[\begin{array}{ccc}2& 0.25& 0.5\end{array}\right]$

b.

To determine

To compute: BA and interpret the result.

Answer to Problem 80E

  $BA=\left[\begin{array}{cc}1180& 1407.5\end{array}\right]$

The first column of above matrix represents the number of calories burned by 130 −lb person.

The second column of above matrix represents the number of calories burned by 155 −lb person.

Explanation of Solution

Given:

  $B=\left[\begin{array}{ccc}2& 0.25& 0.5\end{array}\right]$

  $A=\left[\begin{array}{cc}472& 563\\ 590& 704\\ 177& 211\end{array}\right]$

  $\begin{array}{c}BA=\left[\begin{array}{ccc}2& 0.25& 0.5\end{array}\right]\left[\begin{array}{cc}472& 563\\ 590& 704\\ 177& 211\end{array}\right]\\ =\left[\begin{array}{cc}2\times 472+0.25\times 590+0.5\times 177& 2\times 563+0.25\times 704+0.5\times 211\end{array}\right]\\ =\left[\begin{array}{cc}1180& 1407.5\end{array}\right]\end{array}$

The first column of above matrix (1180) represents the number of calories burned by 130 −lb person.

The second column of above matrix (1407.5) represents the number of calories burned by 155 −lb person.