Homework 1, due January 21, 2008.

Due Wednesday, January 21, 2008.
Post Reply
goodwine
Site Admin
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:

Homework 1, due January 21, 2008.

Post 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.
Bill Goodwine, 376 Fitzpatrick
goodwine
Site Admin
Posts: 1596
Joined: Tue Aug 24, 2004 4:54 pm
Location: 376 Fitzpatrick
Contact:

Re: Homework 1, due January 21, 2008.

Post 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.
Bill Goodwine, 376 Fitzpatrick
Post Reply

Return to “AME 30315, Homework 1”