Example 3

Draw a directed graph to represent the information in the matrix.

To → A B C C = From → A B C [ 1 1 1 1 0 1 0 0 0 ] table with 2 rows and 1 column , row1 column 1 , table with 1 row and 3 columns , row1 column 1 , table with 1 row and 1 column , row1 column 1 , cap to rightwards arrow , end table eh , column 2 b , column 3 c , end table , row2 column 1 , c equals . table with 3 rows and 1 column , row1 column 1 , table with 1 row and 1 column , row1 column 1 , cap from , rightwards arrow , end table eh , row2 column 1 , b , row3 column 1 , c , end table . table with 1 row and 1 column , row1 column 1 , . matrix with 3 rows and 3 columns , row1 column 1 , 1 , column 2 1 , column 3 1 , row2 column 1 , 1 , column 2 0 , column 3 1 , row3 column 1 , 0 , column 2 0 , column 3 0 , end matrix , end table , end table

Image Long Description

Exercises

Write a matrix to represent each finite or directed graph.

1. 
   Image Long Description
2. 
   Image Long Description
3. 
   Image Long Description
4. 
   Image Long Description
5. 
   Image Long Description
6. 
   Image Long Description

Draw a directed graph to represent the information in each matrix.

7. J K L M J K L M [ 0 0 0 1 0 0 1 1 0 1 0 1 1 1 1 0 ] table with 2 rows and 1 column , row1 column 1 , table with 1 row and 4 columns , row1 column 1 , j , column 2 k , column 3 l , column 4 m , end table , row2 column 1 , table with 4 rows and 1 column , row1 column 1 , j , row2 column 1 , k , row3 column 1 , l , row4 column 1 , m , end table . table with 1 row and 1 column , row1 column 1 , . matrix with 4 rows and 4 columns , row1 column 1 , 0 , column 2 0 , column 3 0 , column 4 1 , row2 column 1 , 0 , column 2 0 , column 3 1 , column 4 1 , row3 column 1 , 0 , column 2 1 , column 3 0 , column 4 1 , row4 column 1 , 1 , column 2 1 , column 3 1 , column 4 0 , end matrix , end table , end table
8. A B C D A B C D [ 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 ] table with 2 rows and 1 column , row1 column 1 , eh b c d , row2 column 1 , table with 4 rows and 1 column , row1 column 1 , eh , row2 column 1 , b , row3 column 1 , c , row4 column 1 , d , end table . table with 1 row and 1 column , row1 column 1 , . matrix with 4 rows and 4 columns , row1 column 1 , 0 , column 2 0 , column 3 1 , column 4 1 , row2 column 1 , 1 , column 2 1 , column 3 0 , column 4 0 , row3 column 1 , 0 , column 2 1 , column 3 0 , column 4 1 , row4 column 1 , 1 , column 2 0 , column 3 1 , column 4 0 , end matrix , end table , end table
9. N 1 N 2 N 3 N 4 N 1 N 2 N 3 N 4 [ 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 ] table with 2 rows and 1 column , row1 column 1 , table with 1 row and 4 columns , row1 column 1 , n sub 1 , column 2 n sub 2 , column 3 n sub 3 , column 4 n sub 4 , end table , row2 column 1 , table with 4 rows and 1 column , row1 column 1 , n sub 1 , row2 column 1 , n sub 2 , row3 column 1 , n sub 3 , row4 column 1 , n sub 4 , end table . table with 1 row and 1 column , row1 column 1 , . matrix with 4 rows and 4 columns , row1 column 1 , 0 , column 2 0 , column 3 1 , column 4 1 , row2 column 1 , 1 , column 2 1 , column 3 0 , column 4 0 , row3 column 1 , 0 , column 2 1 , column 3 0 , column 4 1 , row4 column 1 , 1 , column 2 0 , column 3 1 , column 4 0 , end matrix , end table , end table

10. Travel Alice and Becky live on Parkway East, at the intersections of Owens Bridge and Bay Bridge, respectively. Carl and David live on Parkway West, at the intersections of Bay Bridge and Owens Bridge, respectively. Parkway East is a one-way street running east. Parkway West is one-way running west. Both bridges are two-way.

    1. Draw a directed graph indicating road travel between the houses.
    2. Write a matrix T to represent the information in the directed graph.
    3. Writing Calculate T 2 . t squared , .  What does the matrix model? Explain.

Table of Contents