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Homework Help: Linear Transformation

  1. Feb 24, 2007 #1
    Need some help getting started...

    Let T ={ [1, 0], [1, 1] }be a basis for R2 .
    Given that Transition matrix P s←t
    [ 2, 3 ; -1, 2],

    find the basis S for R2.

    Here is what I think...I started by letting v being any vector...

    [1,0] and [0,1] and applied them to the transition matrix by multiplying the transition matrix to each individual set list at the beginning of this sentence to find the v value... to get [2,-1] and [3, 2]

    Then taking these values to the vectors of T

    I get 2*[1,0]-1*[1,1] and
    3*[1,0]+2*[1,1]

    My final answer came up with [1, -1] and [5, 2], so is this the basis of S?


    2)
    Let S ={ [1, -1], [1, 1] } be a basis for R2 .
    Given that Transition matrix P s←t

    [ 1, 2; 2, 3]

    find the basis T for R2.

    I think you have to inverse the trans matrix then do the steps from problem one...I get T={[-1,5], [1,-3]} for basis.
     
  2. jcsd
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