MATLAB Tutor

Part 8: Matrices

1. To enter a matrix in MATLAB, use square brackets. Enter
   
        [1 0 5
         2 8 7
         4 4 9]
   
   Just leave spaces between the row entries, and press Enter at the end of each row.
2. To give your matrix a name, enter
   
        A = ans
3. Enter
   
        M = [2 2  3 4
                1 0 -9 5]
4. Enter
   
        format rational
        H = hilb(9)

The Hilbert matrix is a certain kind of matrix. You do not need to know its definition right now. The important thing to note is that, if a matrix is too big to fit on the screen, MATLAB will break it up into smaller sections for display.

5. Enter
   
        A = hilb(5)
6. Enter
   
        A(2,3)
7. Enter
   
        A(4, : )
8. Enter
   
        A( : , 1)

Note that MATLAB uses the colon as a "wild card." A(4, : ) means "A (4, anything)," or the elements of matrix A, in row 4, and all the columns – so you get all of row 4 of A. Similarly, A(:,1) represents column 1 of A.

9. Ask MATLAB to display row 3 of A, then display column 5. Display only the entry in row 5, column 5.
10. Enter
    
         2 : 7
    
    and write a comment to describe what happens.
11. Enter
    
         2 : 3 : 8
    
    and describe the result.
12. Enter
    
         1 : 2 : 10
    
    Did you get what you expected?
13. You can use this technique to display columns 2 through 4 of matrix A, for instance. Enter
    
         A ( : , 2:4)
14. Enter a command that will display the first three rows of A.
15. Enter
    
         R = [2 3 6
                 4 4 4]
    
    Enter
    
         S = [1 0 0
                 0 1 0]
    
    Enter
    
         T = [4 -1
                 2  1
                 0  5]
16. Enter
    
         R'     % Transpose

    Enter
    
         T'

17. Enter
    
         2 * R
    
    and describe what happens.
18. Enter
    
         2R
    
    and describe what happens.
19. Enter
    
         R + S
20. Enter
    
         R - S
21. Enter
    
         S*T
    
    Enter
    
         T*S
    
    Enter
    
         ST
    
    Remember that you must always use an asterisk to indicate multiplication – of one real number by another, or of a matrix by a constant, or of a matrix by another matrix.
22. Enter
    
         R*S
    
    What happens?
23. Enter
    
         U = [1 2 3; 0 2 3; 0 0 3]
    
    and note what happens. You may use this shortcut method for entering matrices if you like.
24. Enter
    
         I_4 = eye(4)
         I_6 = eye(6)
         Z_2 = zeros(2)
         Z_5 = zeros(5)
    
    These matrix definitions are built into MATLAB; you may use them whenever you need these special matrices.

modules at math.duke.edu

Copyright CCP and the author(s), 2000