Category: Assignment Instructions (Page 1 of 5)

Comment due Sunday, April 29

Test #3 will be given in class Monday, May 6. The format will be similar to the format of Test #1 and Test #2.

Recall from Test #1 and Test #2 that Question #1 asked you a series of conceptual true/false questions where you had to justify your answer. Question #2 asked you for a series of examples of mathematical objects (mostly matrices) satisfying certain conditions.

To prepare for Test #3, for this week’s OpenLab assignment, you will comment on this post with two questions that you come up with yourself, as well as their answers.

1. Your first question should be conceptual and phrased as a statement which is either always true or always false. Your answer should indicate whether the statement is true or false together with a sentence explaining the answer.
2. Your second question should be asking for an example of a mathematical object satisfying certain conditions. Your answer should provide this example together with together with a sentence explaining the example and why it satisfies the conditions.

You can use the Test #1 and Test #2 questions for inspiration (the different versions of the tests had similar questions, so check out your classmates’ solutions here and here for the other versions).

Try to focus on the material covered in class since Test #2. You can see the list of topics on the schedule.

Comment due Sunday, April 14

After last Friday’s magnitude 4.8 earthquake centered in New Jersey, I became curious about how linear algebra is applied in earthquake science. Most of what I found online was not quite relevant for us: the algebra often referred to is not linear (for example, when using triangulation to locate an earthquake’s epicenter, a system of quadratic equations is used… even ChatGPT got confused about this when I asked it for help).

However, I did find one topic that appears to use linear algebra: Geiger’s method for locating the hypocenter of an earthquake. We commonly refer to the epicenter of an earthquake as its location, but the epicenter is a point on the surface of the earth; an earthquake actually originates at some depth below the epicenter at its hypocenter. So, while the epicenter requires only two spacial coordinates, the hypocenter requires three spacial coordinates.

I am not an expert, but I have found a few resources that should help us understand Geiger’s method for locating the hypocenter of an earthquake:

• This assignment from an earth sciences class at the Saint Louis University Earthquake Center (this looks like a draft, watch out for typos!),
• This article (if you have seen partial derivatives in your differential equations or Calculus II class, this might make more sense to you),
• This article (the section on Geiger’s method looks similar to the section on Geiger’s method in the previous article).

For this assignment, you do not have to read any of these resources thoroughly (unless you want to). Read just the section on Geiger’s method in one of these resources (or another one if you find one) and try to understand:

1. what the variables represent,
2. where the equations in the linear system and/or matrices come from,
3. what the solutions of the linear system and/or matrix equations represent,
4. the steps in the procedure (this is an iterative method, which means it’s probably applied more than once).

By the way, some of these resources mention finding the “least squares solution” of a matrix equation; you can read more about that procedure here.

Don’t worry about understanding everything completely or getting everything right. Comment on this post with your ideas about items 1-4 above. If you’re not confident about one or more of them, no problem, you can just say so. Read your classmates’ comments and comment if you agree or disagree with any of their ideas. This should be a conversation among you and your classmates to try to understand this application of linear algebra, even if that understanding is just at a surface level at first.