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MATH 223/ENGR 123 – Matlab Lab #6
Some useful Matlab commands for this assignment:
rref(A)
will reduce a matrix A to its reduced row echelon form
null(A,′r′)
will find a rational basis for null A
rank(A)
returns the rank of a matrix A
x=A\b
solves the linear system Ax = b (A is an m × n matrix; x is
an n × 1 column vector; b is an m × 1 column vector)
rref([A b])
another way to solve Ax = b ([A b] is an augmented matrix)
inv(A)
finds the inverse (if it exists) of a square matrix A
eye(n)
Creates the n × n identity matrix
A′
transpose of A
save lab2
saves variables and their current values to a file called
“lab2.mat”. Note: this only saves (stores) the variables. To
save the Command Window input/output, use the diary
command below.
No file extension is needed (the *.mat extension is added
automatically)
load lab2
loads the saved variables and values from the file “lab2.mat”
(assuming the file exists)
diary labsession.txt Saves a copy of the subsequent text that appears in the
Command Window (input/output) as a text file called
labsession.txt. If the labsession.txt file already exists, the
diary command will append or add on to the end of the file.
Note: The diary command only stores the input/output text
of the Matlab session. It does not store the variables used in
the session. Use the save/load commands above to
store/load variables.
diary off
closes the diary file
clear
clears all variables from memory
Use any of the Matlab commands given above to help you complete the following exercises.
Include a copy of your work done in Matlab in addition to your handwritten solutions.
Save a copy of your commands in an M-file. Make sure the “Current Folder” is “H:\”. To read
more about M-file: http://people.stfx.ca/mlin/engr123/labs/Saving_Matlab_work.pdf or
http://ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Mfile
1. Show that set
is a basis for
.
Con’d…
2. For a given vector v, the vector
(defined in Q1).
Let
a)
b)
c)
d)
denotes the coordinates of v relative to the basis T
and
. Find the following:
, where
, where
. Is it true that
. Is it true that
? (yes or no)
? (yes or no)