Discussion area for final exam practice problems
On question 6 when I find the upper triangular form of the matrix, I should be able to see the eigenvalues on the diagonal of the matrix. What I have is (1,2,0). But the right answer is (2,4,0). I am not sure what I am missing here.
You've probably already figured it out, but I think when you do the row operations, you are changing the eigenvalues. If you were asked to find the eigenvalues of a matrix that was already in upper triangular form, it would work to just use the diagonal entries, but not after you do row operations. (1,2,0) are the eigenvalues for the new matrix you found through row reduction. Mjustiso
On problem 2, I noticed that in matrix form, both i and ii had one column that had a common multiple (1 for the 3rd column of i and 3 for the 3rd column of ii). Is that a quick way to see that they are not independent or does that not always hold true? I can quickly see that i has a det of 0 and calculated ii to get the same - I was just wondering if there's a quicker way? Thanks, Tlouvar
Nevermind. I changed the 7 to an 8 on ii and did not get a zero determinant, so I've answered my own question above. Tlouvar
Is there a place in the book that talks about #20 in the practice problems? It wasn't obvious to me how to calculate the coefficient and was seeing if there was a place I could read up on it.
From Steve Bell: I mentioned in my last review that there won't be any questions about complex Fourier Series on the Final Exam. There might, however, be questions about the complex Fourier TRANSFORM.
Just to confirm I'm doing this right. For number 16, I'd take the Laplace transform of each side, solve for Y(s), then do the inverse Laplace transform of Y(s), then plug in 2 for t?
Disregard, I answered the question for myself.
On problems 16 & 17, I'm having trouble getting them converted back from the Laplace domain. Any tips?
Also on problem 19, isn't B an offset even function too?
Thanks, Tlouvar
To help with 16 and 17, the examples in lessons 20 and 21 are fairly similar. For 19, I think for a function to be even, it has to be symmetric about the y axis, f(-x)=f(x), so the fact that it's offset would make f(-x) not equal to f(x). Mjustiso
