MATLAB stands for MATrix LABoratory. MATLAB is a computer
program that can be very helpful in solving the sorts of
mathematical problems you will frequently encounter throughout your
engineering or technology coursework
First, Change your working directory to your UT H-Drive by the
following steps.
Look for Current Directory. Click on the sign "..." (Browse
Folder)
Move down the cursor to find your UTAD H-Drive
(yourutadusername.utoledo.edu ...(H:)
Now your current are under your UTAD H Drive.
Now create a MATLAB directory by (right) clicking your
mouse on the blank spot of Current Directory. Then select New =>
Folder. Then change the name to MATLAB. This is where you save your
work. You can create other folders later if you want to organize
your files.
Entering and Displaying a Matrix
The MATLAB prompt is >>
To enter a matrix:
start with [
separate elements of the matrix with space (or comma)
use ; (semicolon) to mark end of each row
end the matrix with ]
Example 1Enter matrix
A =
é ê
ê ë
1
2
3
4
5
6
ù ú
ú û
into work space.
Solution:
Type the following, followed by Enter (or return key).
>> A = [ 1 2 3 ; 4 5 6]
You should see
A =
é ê
ê ë
1
2
3
4
5
6
ù ú
ú û
Exercise 2Enter and display the following matrices in MATLAB.
MATLAB can be used to perform the matrix algebra. The symbols for
standard operations are:
Addition: + Substraction: - Multiplication: *
Power: Ù Transpose: ¢
We will use the matrices we have constructed so far to do the
following examples.
Example 1
Compute AB , AT, B2, AC and D = BC. What happen if you try DC?
Solution:
>> A * B
ans =
é ê
ê ë
30
36
42
66
81
96
ù ú
ú û
>> A¢
ans =
é ê ê
ê ë
1
4
2
5
3
6
ù ú ú
ú û
>> BÙ2
ans =
é ê ê
ê ë
30
36
42
66
81
96
102
126
150
ù ú ú
ú û
>> A*C
ans =
é ê
ê ë
22
28
49
64
ù ú
ú û
>> D = B*C
D =
é ê ê
ê ë
22
28
49
64
76
100
ù ú ú
ú û
>> D*C
??? Error using = Þ mtimes Inner matrix dimensions
must agree.
Since DC doesn't make sense, You will see the error information.
Now the matrices C and D have the same dimension. We can do the
following example.
Example 2
Compute C+D and 2C - 3D.
Solution:
>> C+ D
ans =
é ê ê
ê ë
23
30
52
68
81
106
ù ú ú
ú û
>> 2*C - 3 *D
ans =
é ê ê
ê ë
-64
-80
-141
-184
-218
-288
ù ú ú
ú û
Don't forget * sign when you multiply a number with a matrix.
Exercise 3
Compute B3 - 15 B2 - 18 B.
Ordinarily, MATLAB displays up to 5 digits for each number. The
following commands allow you to modify this standard display
style. format Standad display format short Scaled fixed point format with 5 digits. format long Scaled fixed point format with 15 digits for
double and 7 digits for single. format short e Floating point format with 5 digits. format long e Floating point format with 15 digits for double and
7 digits for single. format rat Display the number in fraction as close as
possible.
Use help format to see other formatting options.
MATLAB has a matrix inverse function inv(A).
Example 1
Find the inverse of the matrix
A =
é ê ê
ê ë
1
1
1
5
1
1
2
3
4
ù ú ú
ú û
and also try different
formats.
Solution: First, we input the matrix A by
>> A = [ 1 1 1 ; 5 1 1 ; 2 3 4].
Then >> inv(A)
You should see
ans =
é ê ê
ê ë
-0.2500
0.2500
0
4.5000
-0.5000
-1.0000
-3.2500
0.2500
1.0000
ù ú ú
ú û
Now try
>> format rat
>> inv(A).
You should see
ans =
é ê ê
ê ë
-1/4
1/4
0
9/2
-1/2
-1
-13/4
1/4
1
ù ú ú
ú û
.
5 Submatrices, Rows and Columns of a Matrix and other commands
A(i,j): returns the ij entry of the matrix A
A(i,:): returns the i-th row of A
A(:, j): returns the j-th column of A.
A(p:q, r:s): returns the submatrix from row p to row j and
column r to column s. (Here p £ q and r £ s.)
rref(A): returns the row reduced echelon form of A.
eye(n): returns a n ×n identity matrix.
zeros(n): returns a n ×n zero matrix.
rand(n): returns a n ×n random matrix.
You can save a record of every stroke you make, along with MATLAB's
responses, in a file you choose by turning on the "diary" feature.
For instance, if you select the file name project.txt.
Use the command:
>> diary project.txt
Now let's do something. Say
>> A = [ 1 1 1 ; 5 1 1 ; 2 3 4].
Now type >> diary project.txt again.
You can open the file project.txt to see what has been recorded.
You can also use "diary off" to suspend it and "diary on" turns it
back on.
A script M-file is just a sequence of MATLAB commands stored in a
text file that has ".m" as its extension. You can use the m editor
on MATLAB to create a m file or any other text editor (like notepad
but not WORD). After creating a m-file, you just need to type the
name of the file to run the command in the m-file.
Example 1
Create a m-file named project1.m that creates a matrix
A =
é ê ê
ê ë
1
2
1
1
2
2
2
1
3
ù ú ú
ú û
and compute A3-6A2+5A.
Solution: First find a text editor on your computer.
Type the following:
echo on
A = [ 1 2 1 ; 1 2 2 ; 2 1 3 ]
AÙ 3 - 6 * AÙ 2 + 5 * A
echo off
Then save the file as project1.m to your working directory.
Note that each command is in different lines.
Now type project1.
You should see the results. If you skip ëcho on" and ëcho
off", you will just see the final results (you won't see A).
In your m-file, you can write comment by adding a percent sign.
For example, you can type
% This is my first MATLAB project.
in the beginning of the
project.m file.
Now you can combine the feature of diary and M file to create
a report.
Try
>> diary project1.txt
>> project1
>> diary project1.txt
Now you have a text file that shows all your work.
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version 3.72. On 20 Feb 2008, 08:35.