There will be a homework assignment for Week #6, but it's likely I won't get to post it until Monday, or maybe Sunday evening. If you are anxious to get started, you can be sure that the problems 7.3.6 and 7.3.10 will be on it. You can get to work on those.
UPDATE: The assignment has been posted. It does, indeed, include 7.3.6 and 7.3.10. You can follow the link from the Schedule Page to find out the other problems.
12 comments:
For eigenvectors, does the order/sign of the elements of the vector matter in the following example?
Is x(1,0,-2) be the same as x(-1,0,2) since it can just be multiplied by -1 to get the original vector?
No the sign doesn't matter. If x is an eigenvector for a particular eigenvalue then ax is also an eigenvactor, provided a is not 0.
In your particular example both vectors would be eigenvectors.
are we expected to factor trinomials with no help in problem 7.3.22?
Can someone refresh my memory as to how we use pplane to represent the graph of the differential equations that involve vectors?
Thanks
On the homework 6 assignment page, Friday is the 23rd of February, not the 24th.
RE: Can someone refresh my memory as to how we use pplane to represent the graph of the differential equations that involve vectors?
You can just think of the matrix equation as a system of differential equations if you multiply out the vector. Obviously this only works if we have 2x2 matrices.
Random question:
I know for the first couple questions it asks for the linear dependency of certain column vectors. Do you actually want us to calculate and prove it? Or can we use MATLAB using the rank function?
Thanks!
OK, a couple of answers
Anonymous: for 7.3.22, Yes we expect you to be able to factor a third degree polynomial. You just need one root, try a couple of guesses like -1, 1 or 2 etc. If 1 is a root then you can factor (x-1) and then you have a 2nd deg poly and so on.
c: Yes you have to set up the matrix and show that it either has a non-zero solution or not. You are free to verify your answers with matlab, but at this point in the course you have to show all work.
err, any help with getting the linear system dependent on t to work with pplane?
I second that... I can't figure it out. The program doesn't seem to resemble the equations we have to input AT ALL. Help, please?
I don't know if this helps, but it worked for me. Think of the vectors as
x = (a , b) and
x' = (a' , b')
and use a and b as variables in pplane.
So in 7.5.2, you would graph the equations
a' = 1a - 2b and
b' = 3a - 4b
to get your phase plane! :)
Ok, more answers
anonymous, anonymous & michael: PPLANE does not work when the right hand side depends on t, only x and y. However this is not the case for these problems. When the diffeq is given in matrix form you have to convert it to a system before you input it into pplane as michael pointed out.
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