Chapter 8.2, Problem 74E

a.

To determine

Organize the times spent exercising in a matrix $B$ .

Answer to Problem 74E

  $B=[\begin{array}{ccc}2& 0.25& 0.50\end{array}]$

Explanation of Solution

Given information:

The numbers of calories burned by individuals of different body weights while performing different types of exercises for a one-hour time period are represented by $A$ .

A 130-pound person and a 155-pound person played basketball for 2 hours, jumped rope for 15 minutes, and lifted weights for 30 minutes. Organize the times spent exercising in a matrix $B$ .

Calculation:

The number of calories burned by an individual of different body weights while performing different type of exercises ie represented by

  $A=\begin{array}{cc}475& 563\\ 590& 704\\ 177& 211\end{array}$

Here both persons played basketball for $2$ hours, jumped rope $15\min .=0.25hr.$ and lifted weight for $60\min .=0.50hr$

Hence, the time spent on each exercise by each person is represented by a matrix

  $B=[\begin{array}{ccc}2& 0.25& 0.50\end{array}]$

b.

To determine

Compute $BA$ and interpret the result.

Answer to Problem 74E

  $\boxed{BA=\left[\begin{array}{cc}1180& 1470.5\end{array}\right]}$ which represents the time spent on exercises by each person.

Explanation of Solution

Given information:

The numbers of calories burned by individuals of different body weights while performing different types of exercises for a one-hour time period are represented by $A$ .

Compute $BA$ and interpret the result.

Calculation:

Now,

  $BA$ = $A=\begin{array}{cc}475& 563\\ 590& 704\\ 177& 211\end{array}$

  $[\begin{array}{ccc}2& 0.25& 0.50\end{array}]$

  $=\left[\begin{array}{cc}2\left(472\right)+0.25\left(590\right)+0.50\left(177\right)& 2\left(563\right)+0.25\left(704\right)+0.50\left(211\right)\end{array}\right]$

  $=\left[\begin{array}{cc}1180& 1470.5\end{array}\right]$

Hence, $\boxed{BA=\left[\begin{array}{cc}1180& 1470.5\end{array}\right]}$ which represents the time spent on exercises by each person.