Chapter 4.1, Problem 34PPS

(a)

To determine

The conversion of the data into matrix with the names of the players along the columns.

Answer to Problem 34PPS

The required matrix is $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]$ .

Explanation of Solution

Given:

The given table is shown in Table 1.

Table 1

Name	Goals	Assists
Amy	8	3
Tama	6	5
Kristen	1	8
Catalina	4	2

Calculation:

From the given table shown in Table 1. The matrix with the names of the players along the columns is,

  $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]$

(b)

To determine

To Find: The sum of the columns.

Answer to Problem 34PPS

The sum of the columns of the matrix is $\left[\begin{array}{cccc}11& 11& 9& 6\end{array}\right]$ .

Explanation of Solution

Consider the matrix,

  $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]$

Then, the sum of the columns is,

  $\begin{array}{c}\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]=\left[\begin{array}{cccc}8+3& 6+5& 1+8& 4+2\end{array}\right]\\ =\left[\begin{array}{cccc}11& 11& 9& 6\end{array}\right]\end{array}$

(c)

To determine

The switched data in the matrix that have the names of the players along the rows.

Answer to Problem 34PPS

The required matrix is $\left[\begin{array}{cc}8& 3\\ 6& 5\\ 1& 8\\ 4& 2\end{array}\right]$ .

Explanation of Solution

Consider the matrix,

  $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]$

Then, the conversion the data into the matrix with the names of the players along the rows is,

  $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]=\left[\begin{array}{cc}8& 3\\ 6& 5\\ 1& 8\\ 4& 2\end{array}\right]$

(d)

To determine

To Find: The sum of the row.

Answer to Problem 34PPS

The matrix for the sum of the row is $\left[\begin{array}{c}11\\ 1\\ 9\\ 6\end{array}\right]$ .

Explanation of Solution

Consider the matrix,

  $\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]$

Then, the sum of the row is,

  $\begin{array}{c}\left[\begin{array}{cccc}8& 6& 1& 4\\ 3& 5& 8& 2\end{array}\right]=\left[\begin{array}{cc}8& 3\\ 6& 5\\ 1& 8\\ 4& 2\end{array}\right]\\ =\left[\begin{array}{c}11\\ 1\\ 9\\ 6\end{array}\right]\end{array}$

(e)

To determine

To Find: The conjecture about the effect on the data when the rows and the columns of the matrix are switched.

Answer to Problem 34PPS

The conjecture is explained.

Explanation of Solution

As the rows and the columns are switched the rows and the columns of the matrix maintains the integrity of the data. This is why the data in part (b) and (d) are same. This is called the transpose of the matrix.