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This introductory lab is a MATLAB Tutorial. Please follow directions and type appropriate commands to learn how to work with MATLAB. Your comments are greatly appreciated.
If you have not visited the page A few NOTES on MATLAB please visit it by clicking on it.
|Type :||diary LAB1.text||WHAT is diary?|
||is the file that you need to submit.|
||% your last name
||% your first name
||%Your MATH 22AL User name
|Ways to enter a vector in matlab
|a) Direct Method: b) Using
||u = [4 1.5 3.9]||to create a 3-element row vector 3-element .|
|Type:||v = [1 2 3.1 5]'||to creates a 4-element column vector.|
|In entering a large vector if you
have to continue onto the next line first type ....
then press enter and continue
onto the next line try this with w in the next input
|Type:||w = [2 2.6 5 1 ...|
|Press Enter then Type
||11.6 9 -8]||to creates a 7-element row vector|
|You may use brackets to combine||two vectors to obtain a larger one|
|Type:||t = [u v']
||to create a 7-element vector.|
Why did we use v' instead of
|Type:||s= [ u' v ]||You will see an error message, because the size of the vectors does not match.|
Ways to enter a matrix in MATLAB
|Type:||A = [1 2 3 ; 3 4 5 ; 4 5 6 ] click here to check||to create a 3 by 3 matrix.|
( Note : You need a space
between the row entries and a semicolon
between the rows.)
|Type:||B = eye(4)||to create a 4 by 4 identity matrix.|
|Type:||C = rand(4)||to create a 4 by 4 matrix with randomly generated entries distributed uniformly between 0 and 1.|
|Type:||D= rand(4,3)||to get a 4 by 3 random matrix .|
|Type:||who||to see a list of your variables.|
|Type:||clear D||to clear the variable D|
|Type:||who||to see if D is cleared or not|
|Type:||D=rand(5)||to create a 5 by 5 random matrix.|
|Type:||D=10*D||to multiply every entry of D by 10.|
|Type:||D=round(D)||to round the entries of D to integers. Now
you have a random matrix with integer entries.
You can do all three
operation with a single command :
|Type:||D=round (10*rand(5))||to get a random matrix with integer entries.|
|Type:||E= magic(3)||to get a 3 by 3 magic matrix. Why it is called magic?|
|Type:||E= magic(4)||to get a 4 by 4 magic matrix. Why it is called magic?|
access or redefine any sub-matrix of a given matrix.
|Type:||A(2,2:3)=[3,4]||to change the entries (2,2) and (2,3) to 3 and 4 respectively.|
|Type:||A||to see the matrix A.|
|Type:||A23=A(2,3)||to see the entry (2,3) of A .|
|Type:||row2=A(2,:)||to see the second row of A. In A(2,:) the symbol colon ":" in second component means select entries from all columns.|
|Type:||col3=A(:, 3)||to see the third column of A. In A(:,3) the symbol ":" means select entries from all rows of A.|
|Type:||subD1=D(2:3, 1:3)||to see a sub-matrix of D consisting of the entries on the second-third row and on the first through third columns.|
|Type:||subD2=D([1 3], 1:3)||to see a sub-matrix of D consisting of the entries on the first and third row and on the first through third columns.|
|Type:||subD3=D(1:2:5, 1:3)||Note that 1:2:5 selects the the first, increments by 2 and then selects 3, increments by 2, selects 5.|
|Type:||subD4=D([1 3 5], 1:3)||This should give you the same submatrix obtained by the previous command subD3=D(1:2:5, 1:3).|
Now type the following and
explain what happened( By typing on a new line to percentage sign %
followed by your comments you may avoid receiving an error
You may check your answer by clicking the appropriate box.
|Type:||A(2,3) = -2||check your answer.|
|Type:||A(2,:) = [0 1 0]||check your answer.|
|Type:||A(3,2:3) = [3 4]||check your answer.|
Sometimes you want Matlab to do computation but not to show the answer on the screen. In this case to avoid a display, put a semicolon " ; " at the end of the line. See the following example:
|Type:||B=[ 6 4; 3 0];||To create another matrix called B, but not display it|
|Type:||B||To see the matrix B|
Working with diagonal
|Type:||diag(A)||to see a vector of diagonal entries of A|
|Type:||diag(ans)||to see a matrix of zeroes with the same diagonal entries as A|
|Type:||diag(diag(A))||to see a matrix of zeroes with the same diagonal entries as A.|
Creating zero matrices
and matrices of ones:
|Type:||ones(3)||to create a matrix of entries 1.|
|Type:||ones(3,4)||to create a 3 by 4 matrix of entries 1.|
Use commands, diag, ones, eye, to construct a 4 by 4 matrix of ones , with 2, 3, 4, and 5 on the main diagonal.
note that you can Add matrices of the same size.
|Type:||diag([ 1 2 3 4])||To create a matrix with diagonal 2, 3,
|Type:||ones( ?) + diag([ 1 2 3 4])|| You need to decide what number to
put for "?".
matrices using small matrices.
|Type:||row1=[ 2 2 2 ]||to create a 1 by 3 matrix ( row vector).|
|Type:||col1=row1'||to create the transpose of r , a 3 by 1 matrix ( column vector).|
|Type:||A=[1 2 3; 3 4 5; 4 5 6]||to see the matrix A|
|Type:||A'||to see the transpose of the matrix A|
|Type:||M=[A ; row1]||to add a new row to A to create a 4 by 3 matrix.|
|Type:||N=[A col1]||to add a new column to A to create a 3 by 4 matrix.|
|Type:||B1=[A N]||to create a 3 by 7 matrix. Note the space between two matrices.|
|Type:||B2=[A ; M]||to create a 7 by 3 matrix.|
|Type:||B3=[A ;N]||Why are you getting an error message?|
|Type:||B4=[A M]||Why are you getting an error message?|
Type b = 3:7 to produces the vector with integer elements : 3, 4, 5, 6 and 7. Step size is one.
Type c = 15:4:35
Type c = 15:4:36
Type c = 15:4:37
Type c = 15:4:38
Type c = 15:4:39
Type c = 15:4:40
The syntax for the colon operator is x = start value : step : stop value
to created [0.2 0.45 0.7 0.95].
Type x = 0.2:0.25:1
If the start and stop values and number of the elements are
known we can use the function linspace.
Type : x = linspace(1.2, 2, 5)will create a 5-element vector with start value of 1.2 and stop value of 2 x =[ 1.2000 1.4000 1.6000 1.8000 2.0000]
You may use linspace to create a table like
Type: x = 0:0.5:6
Type: y = sin(x)
to plot the function.
A general set of commands that will accomplish plotting is ( )
xi = linspace(min(x),max(x),100); % 100 x-valuesYou can use more or less than 100 values but the point is that the combination of linspace and max/min minimizes the need for excessive thinking about creating the vectors and so allows you to think about what the results (the plot in this case) looks like and mean.
yi = spline(x,y,xi); % interpolated y-values
logspace plays the role of linspace but on a logarithmic scale. Logarithmic spacing of elements in a vector is useful when dealing with exponential functions (log-log and semilog plots, in particular. The only difference between logspace and linspace to be aware of is in the definition of the starting and ending values.
Being aware of this feature can eliminate a number of errors and
frustrations in using this function.
Sample commands for elementary row operations
Let N be the 3 by 4
matrix that you built in the last step. Suppose first you
interchange the rows 2 and 3.
|Type:||TEMP= N(2,:)||to store the second row of N as TEMP.|
|Type:||N(2,:) =N(3,:)||to replace the second row of N by the third row of N.|
|Type:||N(3,:) =TEMP||to replace the third row of N by TEMP which was the second row of N .|
Now suppose that you
want to multiply
row of the new matrix N by 5 .
|Type:||N(2,:)=5*N(2,:)||to multiply the second row of N by 5|
Now suppose that you
add -7 times the second row to the third row.
|Type:||N(3,:)=-7*N(2,:)+N(3,:)||to add a multiple of the second row to the third row.|
You will learn about the
following two MATLAB commands later in your Linear
algebra class, type the following commands and see how they
|Type:||rref (C)||to see C after row reduction.|
MATLAB commands for matrix operation
A few helpful MATLAB commands
Number Display Formats
To Finish your LAB
||to stop copying in the file " LAB1.text and saving and closing it|
|Type:||diary off||to exit MATLAB|
|Type:||exit||to exit MATLAB|
Use a local editor (pico) to edit your diary file, then in command line of POINT submit it by typing the following command: