Chapter 6.6, Problem 26PPS

(a)

To determine

To organize: the verbal scores and mathematical scores into two matrices.

Answer to Problem 26PPS

The verbal scores is $V=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509& 502\\ 507& 504\\ 507& 502\\ 512& 504\\ 513& 505\end{array}\right]$ and mathematical scores is $M=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}531& 496\\ 533& 498\\ 534& 500\\ 537& 501\\ 538& 504\end{array}\right]$ .

Explanation of Solution

Given:

A table showing the average SATs scores of males and females is given.

Year	Verbal Score		Mathematical score
	Male	Female	Male	Female
1998	509	502	531	496
2000	507	504	533	498
2002	507	502	534	500
2004	512	504	537	501
2005	513	505	538	504

Calculation:

First we organize verbal score into a matrix V.

Male Female

  $V=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509& 502\\ 507& 504\\ 507& 502\\ 512& 504\\ 513& 505\end{array}\right]$

Next we organize Mathematical score into a matrix M.

Male Female

  $M=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}531& 496\\ 533& 498\\ 534& 500\\ 537& 501\\ 538& 504\end{array}\right]$

Conclusion:

Therefore, the verbal scores is $V=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509& 502\\ 507& 504\\ 507& 502\\ 512& 504\\ 513& 505\end{array}\right]$ and mathematical scores is $M=\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}531& 496\\ 533& 498\\ 534& 500\\ 537& 501\\ 538& 504\end{array}\right]$ .

(b)

To determine

To find: the total score that males and females earned on the SAT’s each year.

Answer to Problem 26PPS

Total score that males and females earned on the SATs each year is $\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}1040& 998\\ 1040& 1002\\ 1041& 1002\\ 1049& 1005\\ 1051& 1009\end{array}\right]$ .

Explanation of Solution

Calculation:

Total score that males and females earned on the SATs each year

  $\begin{array}{l}V+M\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509& 502\\ 507& 504\\ 507& 502\\ 512& 504\\ 513& 505\end{array}\right]+\left[\begin{array}{cc}531& 496\\ 533& 498\\ 534& 500\\ 537& 501\\ 538& 504\end{array}\right]\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509+531& 502+496\\ 507+533& 504+498\\ 507+534& 502+500\\ 512+537& 504+501\\ 513+538& 505+504\end{array}\right]\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}1040& 998\\ 1040& 1002\\ 1041& 1002\\ 1049& 1005\\ 1051& 1009\end{array}\right]\end{array}$

Conclusion:

Therefore, total score that males and females earned on the SATs each year is $\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}1040& 998\\ 1040& 1002\\ 1041& 1002\\ 1049& 1005\\ 1051& 1009\end{array}\right]$ .

(c)

To determine

To express: the difference between the verbal and mathematical scores in a matrix.

Answer to Problem 26PPS

The difference between the verbal and mathematical scores in a matrix is $\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}-22& 6\\ -26& 6\\ -27& 2\\ -25& 3\\ -25& 1\end{array}\right]$.

Explanation of Solution

Calculation:

Difference between the verbal and mathematical on the SATs each year

  $\begin{array}{l}=V-M\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509& 502\\ 507& 504\\ 507& 502\\ 512& 504\\ 513& 505\end{array}\right]-\left[\begin{array}{cc}531& 496\\ 533& 498\\ 534& 500\\ 537& 501\\ 538& 504\end{array}\right]\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}509-531& 502-496\\ 507-533& 504-498\\ 507-534& 502-500\\ 512-537& 504-501\\ 513-538& 505-504\end{array}\right]\\ =\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}-22& 6\\ -26& 6\\ -27& 2\\ -25& 3\\ -25& 1\end{array}\right]\end{array}$

Conclusion:

Therefore, the difference between the verbal and mathematical scores in a matrix is $\begin{array}{c}1998\\ 2000\\ 2002\\ 2004\\ 2005\end{array}\left[\begin{array}{cc}-22& 6\\ -26& 6\\ -27& 2\\ -25& 3\\ -25& 1\end{array}\right]$.