Homework 2, due January 27, 2010.

[goodwine]

Reading: all of chapter 6 in the course text.

Exercises: from THIS HANDOUT (not the purchased book), problems 3 (A2, A4, A6 and A8 only), 4, 5 and 6.

[tmo3290]

For problem 3 we are asked to find the general solution for the odd matrices only. However problem 4 then tells to find a particular solution for A2, A4, A7 and A8; so in the end we will have to solve every matrix in problem 3 except for A6. Is that the way you intended it to be, or should we do something differently in either problem 3 or 4?

[goodwine]

For problem 3 we are asked to find the general solution for the odd matrices only. However problem 4 then tells to find a particular solution for A2, A4, A7 and A8; so in the end we will have to solve every matrix in problem 3 except for A6. Is that the way you intended it to be, or should we do something differently in either problem 3 or 4?

No, that was not intended. I'll change it to be A2, 4, 7 and 8 for both problems. Thanks for pointing that out.

[chunkymonkey]

Should we still do the proof?

[goodwine]

Should we still do the proof?

No, that will be next week.

[ctalley1]

Professor, In solving for the eigenvector when we choose an arbitrary value for one of the values, we have always used 1 as the value, but can we use another value if it's more convenient to avoid fractions elsewhere?

[goodwine]

Professor, In solving for the eigenvector when we choose an arbitrary value for one of the values, we have always used 1 as the value, but can we use another value if it's more convenient to avoid fractions elsewhere?

Yes, that is smart to do.

[mkiener]

Just to clarify what we should do for tomorrow:

3. A2, A4, A7, A8
4. same as above
Not do either 5 or 6

Thanks

[goodwine]

Just to clarify what we should do for tomorrow:

3. A2, A4, A7, A8
4. same as above
Not do either 5 or 6

Thanks

Yes.

[goodwine]

Someone asked me:

I know you said not to do the problems with the repeated eigenvalues since we haven’t covered that in class yet. But in problem 3 part A6, there is a real eigenvalue, two complex eigenvalues, and two repeated real eigenvalues. Should we not do that problem then? Because we also have to do problem 4, which asks to solve parts A2,A4,A7 and A8 using initial conditions. So would it be better to just do A7 in problem 3 instead?

A6 has repeated eigenvalues, but it still has a full set of eigenvectors, so the method covered so far still works.