matlab Lesson 1
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This document introduces basic commands and concepts in Matlab, including how to define matrices and their elements, perform operations on matrices, and save workspaces. It provides examples of defining row vectors, column vectors, and multi-dimensional matrices. It also demonstrates using semicolons to define matrices that span multiple lines, line continuation with ellipses, and accessing individual matrix elements. Finally, it lists 10 practice problems for the reader to define matrices in Matlab and check their results.
![Last modified:January 1, 1970 GMT
An Introduction to Matlab(tm): Lesson 1
Some basic commands you will need:
matlab loads the program matlab into your workspace
quit
quits matlab, returning you to the operating system
exit
same as quit
who
lists all of the variables in your matlab workspace
whos
list the variables and describes their matrix size
NOTE - When using the workstations, clicking on UP ARROW will
recall previous commands. If you make a mistake, the DELETE key OR
the backspace key may be used to correct the error; however, one of
these two keys may be inoperable on particular systems.
'matlab' uses variables that are defined to be matrices. A
matrix is a collection of numerical values that are organized into
a specific configuration of rows and columns. The number of rows
and columns can be any number, for example, 3 rows and 4 columns
define a 3 x 4 matrix which has 12 elements in total. A scalar is
represented by a 1 x 1 matrix in matlab. A vector of n dimensions
or elements can be represented by a n x 1 matrix, in which case it
is called a column vector, or a vector can be represented by a 1 x
n matrix, in which case it is called a row vector of n elements.
The matrix name can be any group of letters and numbers up to 19,
but always beginning with a letter. Thus 'x1' can be a variable
name, but '1x' is illegal. 'supercalafragilesticexpealladotious'
can be a variable name; however, only the first 19 characters will
be stored! Understand that 'matlab' is "case sensitive", that is,
it treats the name 'C' and 'c' as two different variables.
Similarly, 'MID' and 'Mid' are treated as two different variables.
Here are examples of matrices that could be defined in 'matlab'.
Note that the set of numerical values or elements of the matrix are
bounded by brackets ......[ ].
c = 5.66 or c = [5.66]
c is a scalar or
a 1 x 1 matrix
x = [ 3.5, 33.22, 24.5 ]
x is a row vector or
1 x 3 matrix
x1 = [ 2
x1 is column vector or](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-1-320.jpg)
![5
3
-1]
A=[1 2 4
2 -2 2
0 3 5
5 4 9]
4 x 1 matrix
A is a 4 x 3 matrix
An individual element of a matrix can be specified with the
notation A(i,j) or Ai,j for the generalized element, or by A(4,1)=5
for a specific element.
When 'matlab' prints a matrix on the monitor, it will be organized
according to the size specification of the matrix, with each row
appearing on a unique row of the monitor screen and with each
column aligned vertically and right-justified.
The numerical values that are assigned to the individual elements
of a matrix can be entered into the variable assignment in a number
of ways. The simplest way is by direct keyboard entry; however,
large data sets may be more conveniently entered through the use of
stored files or by generating the element values using matlab
expressions. First, we will look at the use of the keyboard for
direct entry.
KEYBOARD DEFINITION OR ENTRY FOR A MATRIX
A matrix can be defined by a number of matlab expressions. Examples
are listed below for a 1 x 3 row vector, x, whose elements are
x(1) = 2, x(2) = 4 and x(3) = -1.
x = [ 2 4 -1 ]
or x=[2 4 -1]
or
x = [ 2,4,-1 ]
(A keystroke 'enter' follows each of the above matlab statements.)
Notice that brackets must be used to open and close the set of
numbers, and notice that commas or blanks may be used as delimiters
between the fields defining the elements of the matrix. Blanks used
around the = sign and the brackets are superfluous; however, they
sometimes make the statement more readable.
A 2x4 matrix, y, whose elements are y(1,1)=0, y(1,2) = y(1,3) = 2,
y(1,4) = 3, y(2,1) = 5, y(2,2) = -3, y(2,3) = 6 and y(2,4) = 4 can
be defined](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-2-320.jpg)
![y=[0223
5 -3 6 4 ]
or
y = [ 0 2 2 3 ; 5 -3 6 4 ]
The semicolon ";" is used to differentiate the matrix rows when
they appear on a single line for data entry.
The elements of a matrix can be defined with algebraic expressions
placed at the appropriate location of the element. Thus
a = [ sin(pi/2) sqrt(2) 3+4 6/3 exp(2) ]
defines the matrix
a = [ 1.0000 1.4142 7.0000 2.0000 7.3891 ]
A matrix can be defined by augmenting previously defined matrices.
Recalling the matrix, x, defined earlier
x1 = [ x 5 8 ] creates the result
x1 = [ 2 4 -1 5 8 ]
The expression
x(5) = 8
creates
x = [ 2 4 -1 0 8 ]
Notice that the value "0" is substituted for x(4) which has not
been explicitly defined.
Recalling the definition of matrix, y, above, the expressions
c=[4 5 6 3]
z = [ y;c ]
creates
z=[0 2 2 3
5 -3 6 4
4 5 6 3]](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-3-320.jpg)
![Note that every time a matrix is defined and an 'enter' keystroke
is executed, matlab echoes back the result. TO CANCEL THIS ECHO,
THE MATLAB COMMAND LINE CAN INCLUDE A SEMICOLON AT THE END
OF THE
LINE BEFORE THE KEYSTROKE 'ENTER'.
z=[y;c];
LINE CONTINUATION
Occasionally, a line is so long that it can not be expressed in
the 80 spaces available on a line, in which case a line
continuation is needed. In matlab, the ellipsis defining a line
continuation is three successive periods, as in "...". Thus
4 + 5 + 3 ...
+ 1 + 10 + 2 ...
+5
gives the result
ans = 30
Notice that in this simple arithmetic operation, no matrix was
defined. When such an operation is executed in matlab, the result
is assigned to the matrix titled "ans". A subsequent operation
without an assignment to a specific matrix name will replace the
results in 'ans' by the result of the next operation. In the above,
'ans' is a 1x1 matrix, but it need not be so in general.
BEFORE YOU QUIT THIS SESSION !!!!!
If this is your first lesson using matlab, execute the matlab
commands 'who' and whos' before you 'quit'. Note that each of these
commands lists the matrices you have defined in this session on the
computer. The command 'whos' also tells you the properties of each
matrix, including the number of elements, the row and column size
(row x column) and whether the elements are complex or real.
IMPORTANT! If you execute the matlab command 'save' before you
quit, all of the matrices that have been defined will be saved in
a file titled matlab.mat stored in your workspace. Should you
desire to save specific matrices during any session, the command
'save' followed by the name of the matrix can be executed. More
detail on how to save and recall your matrices is discussed in
Lesson 2.](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-4-320.jpg)
![PRACTICE PROBLEMS
Determine the size and result for the following matrices.
Subsequently, carry out the operations on matlab that define the
matrices, and check your results using the 'whos' statement.
1. a = [1,0,0,0,0,1]
2. b = [2;4;6;10]
3. c = [5 3 5; 6 2 -3]
4. d= [3 4
5 7
9 10 ]
5. e = [3 5 10 0; 0 0 ...
0 3; 3 9 9 8 ]
6. t = [4 24 9]
q = [t 0 t]
7. x = [ 3 6 ]
y = [d;x]
z = [x;d]
8. r = [ c; x,5]
9. v = [ c(2,1); b ]
10. a(2,1) = -3 (NOTE: Recall matrix "a" was defined in (1)
above.)
Back to Matlab In-House Tutorials](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-5-320.jpg)
![PRACTICE PROBLEMS
Determine the size and result for the following matrices.
Subsequently, carry out the operations on matlab that define the
matrices, and check your results using the 'whos' statement.
1. a = [1,0,0,0,0,1]
2. b = [2;4;6;10]
3. c = [5 3 5; 6 2 -3]
4. d= [3 4
5 7
9 10 ]
5. e = [3 5 10 0; 0 0 ...
0 3; 3 9 9 8 ]
6. t = [4 24 9]
q = [t 0 t]
7. x = [ 3 6 ]
y = [d;x]
z = [x;d]
8. r = [ c; x,5]
9. v = [ c(2,1); b ]
10. a(2,1) = -3 (NOTE: Recall matrix "a" was defined in (1)
above.)
Back to Matlab In-House Tutorials](https://image.slidesharecdn.com/lesson1-140121212803-phpapp01/85/matlab-Lesson-1-6-320.jpg)
matlab Lesson 1
- 1. Last modified:January 1, 1970 GMT An Introduction to Matlab(tm): Lesson 1 Some basic commands you will need: matlab loads the program matlab into your workspace quit quits matlab, returning you to the operating system exit same as quit who lists all of the variables in your matlab workspace whos list the variables and describes their matrix size NOTE - When using the workstations, clicking on UP ARROW will recall previous commands. If you make a mistake, the DELETE key OR the backspace key may be used to correct the error; however, one of these two keys may be inoperable on particular systems. 'matlab' uses variables that are defined to be matrices. A matrix is a collection of numerical values that are organized into a specific configuration of rows and columns. The number of rows and columns can be any number, for example, 3 rows and 4 columns define a 3 x 4 matrix which has 12 elements in total. A scalar is represented by a 1 x 1 matrix in matlab. A vector of n dimensions or elements can be represented by a n x 1 matrix, in which case it is called a column vector, or a vector can be represented by a 1 x n matrix, in which case it is called a row vector of n elements. The matrix name can be any group of letters and numbers up to 19, but always beginning with a letter. Thus 'x1' can be a variable name, but '1x' is illegal. 'supercalafragilesticexpealladotious' can be a variable name; however, only the first 19 characters will be stored! Understand that 'matlab' is "case sensitive", that is, it treats the name 'C' and 'c' as two different variables. Similarly, 'MID' and 'Mid' are treated as two different variables. Here are examples of matrices that could be defined in 'matlab'. Note that the set of numerical values or elements of the matrix are bounded by brackets ......[ ]. c = 5.66 or c = [5.66] c is a scalar or a 1 x 1 matrix x = [ 3.5, 33.22, 24.5 ] x is a row vector or 1 x 3 matrix x1 = [ 2 x1 is column vector or
- 2. 5 3 -1] A=[1 2 4 2 -2 2 0 3 5 5 4 9] 4 x 1 matrix A is a 4 x 3 matrix An individual element of a matrix can be specified with the notation A(i,j) or Ai,j for the generalized element, or by A(4,1)=5 for a specific element. When 'matlab' prints a matrix on the monitor, it will be organized according to the size specification of the matrix, with each row appearing on a unique row of the monitor screen and with each column aligned vertically and right-justified. The numerical values that are assigned to the individual elements of a matrix can be entered into the variable assignment in a number of ways. The simplest way is by direct keyboard entry; however, large data sets may be more conveniently entered through the use of stored files or by generating the element values using matlab expressions. First, we will look at the use of the keyboard for direct entry. KEYBOARD DEFINITION OR ENTRY FOR A MATRIX A matrix can be defined by a number of matlab expressions. Examples are listed below for a 1 x 3 row vector, x, whose elements are x(1) = 2, x(2) = 4 and x(3) = -1. x = [ 2 4 -1 ] or x=[2 4 -1] or x = [ 2,4,-1 ] (A keystroke 'enter' follows each of the above matlab statements.) Notice that brackets must be used to open and close the set of numbers, and notice that commas or blanks may be used as delimiters between the fields defining the elements of the matrix. Blanks used around the = sign and the brackets are superfluous; however, they sometimes make the statement more readable. A 2x4 matrix, y, whose elements are y(1,1)=0, y(1,2) = y(1,3) = 2, y(1,4) = 3, y(2,1) = 5, y(2,2) = -3, y(2,3) = 6 and y(2,4) = 4 can be defined
- 3. y=[0223 5 -3 6 4 ] or y = [ 0 2 2 3 ; 5 -3 6 4 ] The semicolon ";" is used to differentiate the matrix rows when they appear on a single line for data entry. The elements of a matrix can be defined with algebraic expressions placed at the appropriate location of the element. Thus a = [ sin(pi/2) sqrt(2) 3+4 6/3 exp(2) ] defines the matrix a = [ 1.0000 1.4142 7.0000 2.0000 7.3891 ] A matrix can be defined by augmenting previously defined matrices. Recalling the matrix, x, defined earlier x1 = [ x 5 8 ] creates the result x1 = [ 2 4 -1 5 8 ] The expression x(5) = 8 creates x = [ 2 4 -1 0 8 ] Notice that the value "0" is substituted for x(4) which has not been explicitly defined. Recalling the definition of matrix, y, above, the expressions c=[4 5 6 3] z = [ y;c ] creates z=[0 2 2 3 5 -3 6 4 4 5 6 3]
- 4. Note that every time a matrix is defined and an 'enter' keystroke is executed, matlab echoes back the result. TO CANCEL THIS ECHO, THE MATLAB COMMAND LINE CAN INCLUDE A SEMICOLON AT THE END OF THE LINE BEFORE THE KEYSTROKE 'ENTER'. z=[y;c]; LINE CONTINUATION Occasionally, a line is so long that it can not be expressed in the 80 spaces available on a line, in which case a line continuation is needed. In matlab, the ellipsis defining a line continuation is three successive periods, as in "...". Thus 4 + 5 + 3 ... + 1 + 10 + 2 ... +5 gives the result ans = 30 Notice that in this simple arithmetic operation, no matrix was defined. When such an operation is executed in matlab, the result is assigned to the matrix titled "ans". A subsequent operation without an assignment to a specific matrix name will replace the results in 'ans' by the result of the next operation. In the above, 'ans' is a 1x1 matrix, but it need not be so in general. BEFORE YOU QUIT THIS SESSION !!!!! If this is your first lesson using matlab, execute the matlab commands 'who' and whos' before you 'quit'. Note that each of these commands lists the matrices you have defined in this session on the computer. The command 'whos' also tells you the properties of each matrix, including the number of elements, the row and column size (row x column) and whether the elements are complex or real. IMPORTANT! If you execute the matlab command 'save' before you quit, all of the matrices that have been defined will be saved in a file titled matlab.mat stored in your workspace. Should you desire to save specific matrices during any session, the command 'save' followed by the name of the matrix can be executed. More detail on how to save and recall your matrices is discussed in Lesson 2.
- 5. PRACTICE PROBLEMS Determine the size and result for the following matrices. Subsequently, carry out the operations on matlab that define the matrices, and check your results using the 'whos' statement. 1. a = [1,0,0,0,0,1] 2. b = [2;4;6;10] 3. c = [5 3 5; 6 2 -3] 4. d= [3 4 5 7 9 10 ] 5. e = [3 5 10 0; 0 0 ... 0 3; 3 9 9 8 ] 6. t = [4 24 9] q = [t 0 t] 7. x = [ 3 6 ] y = [d;x] z = [x;d] 8. r = [ c; x,5] 9. v = [ c(2,1); b ] 10. a(2,1) = -3 (NOTE: Recall matrix "a" was defined in (1) above.) Back to Matlab In-House Tutorials
- 6. PRACTICE PROBLEMS Determine the size and result for the following matrices. Subsequently, carry out the operations on matlab that define the matrices, and check your results using the 'whos' statement. 1. a = [1,0,0,0,0,1] 2. b = [2;4;6;10] 3. c = [5 3 5; 6 2 -3] 4. d= [3 4 5 7 9 10 ] 5. e = [3 5 10 0; 0 0 ... 0 3; 3 9 9 8 ] 6. t = [4 24 9] q = [t 0 t] 7. x = [ 3 6 ] y = [d;x] z = [x;d] 8. r = [ c; x,5] 9. v = [ c(2,1); b ] 10. a(2,1) = -3 (NOTE: Recall matrix "a" was defined in (1) above.) Back to Matlab In-House Tutorials