2.3 Addition of Matrices - Problems

1. Using the following matrices, perform the operation indicated when it is defined and state that the operation is not defined for the particular matices when that is the case:
   
   
   1. A + C

   2. D + E

   3. F - D

   4. F + B

   5. B - (A + C)

   6. D - (E + F)

   7. B + C - B

   8. A - D

   9. A + D^T

   10. D + E - B^T

   
   
2. What matrix would need to be added to A to produce the 3 by 5 zero matrix if
   
   
   
   

3. Matrix A represents the number of wins and losses for these teams in one year and B represents the number of wins and losses for the next year.
   
   
   
   
   1. What are the teams' records for the two years combined?
      

   2. Write a sentence about what row 3 tells us.
      

   3. If the three season record for these teams is represented by C, how many games did each team win and lose in the third year?
      
      
      
      

4. Matrix A represents the points scored from three kinds of shots made by each team during the first period of a basketball game, B represents the same information from the second period, C represents the same information from the third period, and E represents the total number of points scored from each of the three kinds of shots in the game by each team. The column for free throws is labeled by FT, field goals by FG, and three-point shots by T.
   1. How many points of each kind were scored by each team in the fourth period? (There are 4 periods in a basketball game).
      
      

      
      

   2. Which team won the game? What was the final score for each team?

5. If A is a square matrix, is A + A^T always symmetric? Explain.

6. If matrices A and B are symmetric and have the same dimensions, is A - B symmetric? Explain.

Write a program that will add and subtract matrices. You may build this on the program that you wrote in Chapter 1. The user should enter the matrices and indicate whether the matrices are to be added or subtracted. You should be able to add or subtract as many matrices as you wish without having to re-enter the previous solution. For example, can your program handle A + B - C + D? Remember that your program should be user-friendly and should have comments in the code. Again, write this program without using any commands that directly read, write, or manipulate matrices.