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Co-ordinate transformation matrix

  1. Nov 10, 2007 #1
    Plz advise if my approach is correct for 1st part and for 2nd part, I need some help.

    Problem Statement

    Consider the linear transformation T: R3->R2 whose matrix with respect to standard bases is given by | 2,1,6 |
    | 0,2,-1|.
    Now consider the bases f1={2,4,0}, f2={1,0,1}, f3 = {0,3,0} in R3 and
    g1 = {1,1} and g2 = {1,-1}

    Compute the coordinate transformation matrices between the standard bases and these bases and compute the matrix of T with respect to the new bases

    Problem solution

    For first part, I am doing the following
    Express u1, u2, u3 in terms of standard bases vectors
    u1 = 2e1 + 4e2;
    u2 = e1 + e3;
    u3 = 3e2;
    Solve for e1,e2,e3 in terms of u1, u2, u3 and transpose of this is my co-ordinate transformation matrix. Is this correct?

    For g vectors, do in a similar manner

    For second part

    I don't understand this part. How do I compute the matrix of T wrt these new bases. Any pointers would be appreciated.
  2. jcsd
  3. Nov 11, 2007 #2
    Look where T takes the new standard basis elements ie equiv of (1,0,0), (0,1,0) etc
  4. Nov 11, 2007 #3
    Don't really understand your response. Could you elaborate plz.

    Also, is my 1st part to solution correct?

  5. Nov 12, 2007 #4


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    Homework Helper

    Look at how exactly the matrix representation of an operator is given.
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