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Linear Algebra! What does it mean?

  1. Apr 19, 2012 #1
    Hello folks, I will keep the whining about this subject short and to the point. I have my final exam tomorrow which is Linear Algebra and is a required subject to get into Chemistry, and the only one I have to take. Linear Algebra has been the anomaly for this semester as I've done well in every other course but this one, even though for a majority of the semester I put in an obscene amount of effort into this course at the expense of Calculus and Chemistry, though I'm pretty sure I will come out of those two courses with B's if not A's. Linear Algebra though, of the 40 marks awarded before the final I only managed to accumulate 17, thanks to a pitiful showing on the first midterm. I therefore need a 54% on the final tomorrow to pass the course, and I'm doubtful I'm going to get that as exam burnout has hit me full force, and I am not particularly comfortable, or interested, with the material. Should I brace myself for a fail and try again? Should I change majors from chemistry? Should I drop out and take a trade? I really am just flipping papers and not really absorbing anything right now. Any advice would be much appreciated. Thanks! :)
     
  2. jcsd
  3. Apr 19, 2012 #2

    jgens

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    Gold Member

    You are not being productive now, so take a break for an hour or two. Take a nap, watch TV, eat some food, etc. Then come back and start studying again.
     
  4. Apr 19, 2012 #3
    What jgens said is really the only thing you can do. In order to improve yourself intellectually, you have to push your brain beyond it's limits. Right now, you've hit an "exam burn out" limit. In order to make your brain able to handle this situation in the future, try to push through it now as hard as possible. Study study study for the exam and try to get past that 54%. Read the textbook, go step by step through your notes, do example problems, do textbook problems, try to prove things the textbook proves for you if you're being tested for proofs. Learn the logic of the material.

    Improve your self!
     
  5. Apr 20, 2012 #4

    chiro

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    Science Advisor

    Hey MarcZZ and welcome to the forums.

    Linear algebra is mostly about studying things that are 'flat' and 'act like arrows'. This is not rigorous but it should give you an idea of what this is all about.

    Vector spaces act in a way with their operations that they act like arrows like when you add two vectors together. If a vector space has an inner product then you can treat things like they were arrows in a geometric space like you do with vectors and because of this you can take a vector space and decompose it into orthogonal components which in non-math speak means finding how many independent variables there are and how to write it out as a linear combination in the same way you write out x = x1e1 + x2e2 + x3e3 where <e1,e2,e3> is the normal x,y,z axis and <x1,x2,x3> are the components for each axis: you can do the same thing for any vector space if it has an inner product and you see this being done for functions as well.

    Now the other important thing to realize is that in calculus, derivatives are linear operators. In your normal y = f(x), the produces a straight line when applied to some x and this is actually the case for any dimension n where n is a finite positive integer (lets just stick to simple cases). Also in multivariable calculus, derivatives act like matrices and this is not surprising considering the derivative is a linear operator.

    Also many problems in different areas reduce down to solving Ax = B for A and B which include many areas of science (including chemistry).

    So to sum up, think of matrices as 'arrow-type' and flat, related to calculus and really useful for analyzing derivatives in n-dimensions, used in geometry (including differential geometry), and also used in any problem where you have to solve Ax = B which you will find everywhere in science, engineering, statistics and other applied fields.

    I am not doing justice for describing every application of linear algebra, but I think this will help you realize how and why it's used.
     
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