
Re: Failing Linear Algebra:
Posted:
Apr 27, 2004 6:03 PM


harrisq@tcs.inf.tudresden.de (Mitch Harris) wrote in message news:<c6e1ep$aov3s$1@uniberlin.de>... > Anonymous wrote: > >I'm currently a math major and am taking linear algebra, but I'm in > >serious danger of failing. I just don't get it! Is this newsgroup a > >place to come to ask questions and get information about learning > >math? > > 1) for informal curiosity questions, sci.math is great > 2) if you expect the sci.math news group to help you consistently every > week on your homework problems, it could happen but it depends on your > doing a lot of the work first and being very conscientious in your > requests for help. > > >Or is there somewhere more appropriate to go? > > Online? hmmm... there might be chatrooms but linear algebra seems at a > level where a dedicated chatroom would be a little sparse. look for > undergrad math tutoring or help. > > > I've always had > >trouble with vectors, and I think I fell apart sort of right at the > >beginning of linear algebra (although, I did manage to get a B on the > >very first exam). I've got another exam next week. What can I do? I > >don't get all the terms, concepts, and jargon. Anyone know how to > >make learning linear algebra easier and more practical? > > Practical? do you mean like showing how it is useful? > 1) the contrite answer is that it is useful for fulfilling the > requirements of a degree in mathematics. > > 2) the liberal arts answer is that it is one of the pillars of > the beautiful and wonderful human achievement that is mathematics (along > with say differential/integral calculus, number theory, or logic). It > permeates all of mathematics. > > 3) the plain answer is that it is used all the time in engineering. > > The answer you probably want though is that to make linear algebra easier > to understand (because it is all symbols, it's so abstract, you can lose > sight of what it really means) is to try to give it an interpretation that > is easier to think about. Usually geometrical/visual interpretations work > best with linear algebra. Think of arrows in the plane or 3space as > vectors, a linear transformation (multiplying by a matrix) as modifying a > set of points,
I've got all that, more or less.
>the determinant is what?
I know how to compute it, at least for 2X2 and 3X3 matrices. Any matrix larger than that can be reduced by getting all 0's and one 1 in any row or column, right? And then it's treated like a 3X3 matrix? Can a 3X3 similarly be reduced to a 2X2? I also know something about the determinant equaling 0 or not equaling 0. If it does, then the equations are independent (?????), I think.
>eignevectors are what?
If T(*x*) = (constant)(*x*), then (*x*) is the eigenvector and (constant [lambda]) is the eigenvalue, right? I still need to understand what has to be done to solve for the eigenvalues and eigenvectors though. I was able to piece together what I had to do for the homework assignments. But, I guess I did it in a very roundabout way. My professor explained that it could just be calculated by multiplying 2 matrices. Still, I don't really understand....
similar > matrices behave how?)
I don't know what a similar matrix is. Is that where one of them equals the other times a scalar? If so, how does one determine if two matrices *are* similar? So, talking here is really making me start to think that maybe it's *not* the concepts and definitions that I'm having major problems with. Maybe it's more the computation and how to solve for something or show whether something is or is not something else (e.g., how to show 2 matrices are similar, how to show whether a system is linearly independent, how to show whatever the determinant is used to show, etc).
etc. ask your TA or prof about these...er after the > test. > > >Anyone got any practice problems? > > Online? possibly (google is your best bet here), but in real life, you can > go to a university library and find "Schaum's outlines" or "thousand's of > problems solved in" for linear algebra.
I've got Schaum's. I don't understand how they solve a lot of the problems....

