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Find basis B given the transition matrix and B'

  1. Apr 6, 2015 #1
    1. The problem statement, all variables and given/known data
    The Matrix P =
    1 0 3
    1 1 0
    0 3 1
    is the transition matrix from what basis B to the basis B' = {(1,0,0),(1,1,0),(1,1,1) for R3?

    2. Relevant equations
    [v]B=P[v]B'

    3. The attempt at a solution
    I'm looking at a theorem in my book that says

    " if P is the transition matrix from a basis B' to a basis B for a finite-dimensional vector space V, then P is invertible and P-1 is the transition matrix from B to B'. "

    So does the inverse of P give the basis B? Please tell me how wrong I am :)
     
  2. jcsd
  3. Apr 7, 2015 #2

    BiGyElLoWhAt

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    Gold Member

    I will gladly tell you how wrong you are. Not at all (if I understand you correctly)
    You have ## \bf{P} \cdot \bf{B} = \bf{B'} ## Multiply both sides by ## \bf{P}^{-1} ## and you have solved your equation for B.
     
  4. Apr 7, 2015 #3
    Awesome, thank you! \m/
     
  5. Apr 8, 2015 #4

    BiGyElLoWhAt

    User Avatar
    Gold Member

    No problemo
     
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