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Homework Help: Vector space help

  1. Oct 13, 2006 #1
    Vector space help plz..

    Hi,
    Just started a linear algebra course recently but I am confused with the notation used :confused:

    http://i9.tinypic.com/2w4za50.jpg

    I am unsure how to proceed with this question. Can someone help? The part highlighted, what does it mean? 2x2 matrix of P? The P represents the polynomial entries? :confused: Can give me an example to give me a head start? Many thanks!
     
  2. jcsd
  3. Oct 13, 2006 #2

    radou

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    Yes, it is the set of all 2x2 matrices whose elements are real polynomials. Start with: http://mathworld.wolfram.com/VectorSpace.html" [Broken].
     
    Last edited by a moderator: May 2, 2017
  4. Oct 13, 2006 #3
    Thanks :smile:

    Is it something like this?

    http://i10.tinypic.com/48qhc1w.jpg
     
    Last edited by a moderator: May 2, 2017
  5. Oct 13, 2006 #4

    radou

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    Yes, it's exactly something like this. :smile: Now just look at the definition of a vector space and at the properties that the addition and scalar multiplication must satisfy to proove if it's a vector space or not.
     
  6. Oct 13, 2006 #5
    thanks for the confirmation again :smile:

    Ok hmm I don't know if I'm on the right track but do I have to have two different matrices? Lets say matrix A and matrix B where A has elements:

    http://i10.tinypic.com/4g7c4lj.jpg

    and B with similar elements in order to check whether they satisfy closure by addition and multiplication? Or have I interpreted the definition totally wrong? :uhh:
     
  7. Oct 14, 2006 #6

    radou

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    You're on the right track.
     
  8. Oct 14, 2006 #7
    Thanks :smile:

    I've just noticed that I've chosen specific polynomials for my matrix entries so is that wrong? what would the matrix look like with general polynomial entries if a degree isn't given? Hmm am i making any sense here :uhh:
     
  9. Oct 14, 2006 #8

    radou

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    You don't have to write down specific polynomials as entries in your matrix. It is enough to write down something like [tex]\left(\begin{array}{cc}p_{1} & p_{2}\\p_{3} & p_{4}\end{array}\right)[/tex], where [tex]p_{i}, i = 1, \cdots, 4[/tex] are your real polynomials, which is the only thing that matters, unlike their degrees.
     
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