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Linear AlgebraMatrix Representation Problem

  1. Dec 4, 2011 #1
    1. The problem statement, all variables and given/known data
    I'm practicing for my finals this coming week and I'm confused about these 2 problems.
    Screen Shot 2011-12-04 at 9.43.11 PM.png
    Screen Shot 2011-12-04 at 9.44.25 PM.png
    2. Relevant equations



    3. The attempt at a solution
    For e). I followed my notes and came up with D=U-1AU..since its asking for some basis to standard basis. And once computed, its the diagonal matrix.

    D=
    [-2 0 0]
    [0 3 0]
    [0 0 1]
    So am I doing it right?

    For part F). I dont know if its exactly the same method as above or do I need to get S=U-1V then B=SAS-1

    I'm confused with all this!
     
  2. jcsd
  3. Dec 5, 2011 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You've cut off the critical information: what "L" is!

    In general, you write a linear transformation, from vector space, V, to itself, as a matrix, in terms of an ordered basis, by applying that linear transformation to each basis vector in turn, writing the result as a linear combination of those basis vectors. The coefficients of each linear combination give a column of the matrix.
     
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