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Homework 1, due January 21, 2008.
Posted: Fri Jan 16, 2009 3:52 pm
by goodwine
Put your ND student ID number on the homework. Putting your name on it is optional.
From the course text, do problems 6.2, 6.3 and 6.4.
Reading: Chapter 6 from the course text.
Important: you must put your student ID number on your homework. The homeworks will be returned outside the elevators on the third floor of Fitzpatrick. You may put your name on it if you want to, but it is optional.
Re: Homework 1, due January 21, 2008.
Posted: Mon Jan 19, 2009 5:36 pm
by goodwine
Someone asked me:
I am confused about one part of our homework during the step of solving (A-lambda*I)*Xi=0. After subtracting Lambda*I from A the matrix is:
0 0 0 0
0 0 1 = 0
0 1 0 0
The matrix cannot be manipulated into an upper-triangular matrix without row switching. This is a problem for me because if I switch rows 1 and 3, the result is different than if I were to switch rows 2 and 3. For example, if I were to switch rows 1 and 3:
0
Xi = 0
1
However, if I were to switch rows 2 and 3:
1
Xi = 0
0
I know from checking both answers that the second Xi is the correct one. What I don't know is why.
When you switch columns, you are also switching the components of xi. If you switch columns 1 and 3, then you need to switch columns 1 and 3 in xi, so the answer is xi=[ 1 0 0 ]. Same if you switch columns 2 and 3.
I think you want to be able to systematically do all the problems, but also don't lose sight of the fact that you can basically do this one by inspection. If you think of the system as three equations, clearly the second and third components must be zero and the first component is arbitrary.