Entering Matrices with MATLAB

For a tutorial on MATLAB that is calculus specific you can point your browser at http://www.math.csi.cuny.edu/MATLAB/tutorial/.

Creating Matrices To create matrices you designate to MATLAB that you want a matrix with the square brackets:

• If you have no punctuation between your numbers you will create a matrix with one row

  >> A = [1 2 3 4]                % the matrix [1 2 3 4]
  >> A = [1, 2, 3, 4]             % the matrix [1 2 3 4]
    

  The same is achieved by putting in commas as the example indicates
• If you use the semicolon ; you can create multiple rows

  >> A = [1 2 ; 3 4]              % 2 rows
  A =
    1  2
    3  4
  >> A = [1 2; 3 4; 5 6]          % 3 rows 
  A =
    1  2
    3  4
    5  6
  >> A = [1 2 3; 4 5 6]           % again 2 rows
  A =
    1  2  3
    4  5  6
  

  Notice you need to have the same number of elements in each row

  >>A = [1 2 3; 4 5]
  error: number of columns must match % oops!
  

  Think about the semicolon as joining rows together. For example look at

  >> B = [ 1 2 3]; C = [4 5 6];   % no output with the trailing ;
  >> A = [B ; C]
  A =
    1  2  3
    4  5  6
  

  So to paste rows together you use a semicolon.

• To paste columns together, we use a comma or no puctuation.

  >> A = [B C]                    % already defined
  A = [1 2 3 4 5 6]
  >> A = [B' C']                  % prime is a transpose
  A =
    1  4
    2  5
    3  6
  

  Here we used the transpose of a matrix which flips the role of rows and columns. For example, with A, B and C as above:

  >> A'
  ans =
    1  2  3
    4  5  6
  >> B'                           % B was [1 2 3], B' is [1 ; 2 ;3]
  ans =
    1
    2
    3
  >> C'
  ans =
    4
    5
    6
  

  Let's see how we form an augmented matrix, This joins a column called b to a matrix A. Suppose we start with the system of equations 5x + 6 y = 7
  4x - 7y = 8 align* Then the matrix A would be the matrix of coefficients, namely

  >> A = [5 6; 4 -7];             % suppress output
  

  The column matrix b contains the constants.

  >> b = [7 8]'                   % notice the transpose
  

  Then we want to join the column vector b to the matrix A by attaching a column

  >> A = [A b]
  A =
     5   6   7
     4  -7   8
  

• This is kind of like a spreadsheet. You specify an element by giving the row number and column number (counting starts with a 1). Remember the row comes first then the column. Start with A from above

  >> A(1,1)                       % gives 5. Notice the parentheses (,)
  >> A(2,3)                       % gives 8
  >> A(3,2)                       % an error. No third row
  

  We can also extract slices by putting lists of numbers

  >> A([1 2],3)                   % A(1,3) and A(2,3)
  ans =
    7
    8
  >> A(2,[1 2])                   % A(2,1) and A(2 2)
  ans =
     4  -7
  

  Slices take time to think about.

Here is a side diversion:

Generating numbers

An important command to generate numbers in a systematic way is to use the colon operator. its syntax is

>> a:b                          % from a to b by 1's
>> a:h:b                        % from a to b by steps of size 'h'

for example the commands below give the output indicated

>> 1:3                          % same as [1 2 3] 
>> 1:2:9                        % gives [1 3 5 7 9]

More on slices

We use these to extract parts of matrices.

For example the ones above could be written

>> A(1:2,3)                   % A(1,3) and A(2,3)
ans =
  7
  8
>> A(2,1:2)                   % A(2,1) and A(2 2)
ans =
   4  -7

Finally, there is a shortcut when you want the entire row or column. Just use a semicolon ``:''

>> A(:,2)
ans =
   6
  -7
>> A(2,:)
ans =
   4  -7   8