Chapter 3.5, Problem 29PPS

(a)

To determine

To calculate: Difference between the American and World records expressed as a matrix.

Answer to Problem 29PPS

  $\left[\begin{array}{c}0.5\\ 0.47\\ 0.87\\ 0\end{array}\right]$

Explanation of Solution

Given information: 

Data of Olympic women freestyle swimming.

Formula used: 

  $\left[\begin{array}{l}a\hfill \\ b\hfill \\ c\hfill \end{array}\right]-\left[\begin{array}{l}d\hfill \\ e\hfill \\ f\hfill \end{array}\right]=\left[\begin{array}{l}a-d\hfill \\ b-e\hfill \\ c-f\hfill \end{array}\right]$

Calculation: 

So the difference of the American and World records is:

  $\left[\begin{array}{c}24.63\\ 53.99\\ 117.41\\ 496.22\end{array}\right]-\left[\begin{array}{c}24.13\\ 53.52\\ 116.54\\ 496.22\end{array}\right]=\left[\begin{array}{c}24.63-24.13\\ 53.99-53.52\\ 117.41-116.54\\ 496.22-496.22\end{array}\right]$

  $\left[\begin{array}{c}0.5\\ 0.47\\ 0.87\\ 0\end{array}\right]$

(b)

To determine

column and row of matrix represent 

Answer to Problem 29PPS

Rows of the matrix represent the timing of different freestyle swimming distances and column of matrix represent the difference between the America time and world record.

Explanation of Solution

Given information:

  $\left[\begin{array}{c}0.5\\ 0.47\\ 0.87\\ 0\end{array}\right]$

Rows of the matrix represent the timing of different freestyle swimming distances and column of matrix represent the difference between the America time and world record.

(c)

To determine

in which fastest time set.

Answer to Problem 29PPS

50 m freestyle swimming

Explanation of Solution

Given information: 

Data in the given table

 

As by the data it can be seen that in 50 m freestyle swimming the fastest time sets.