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Linear Transformations matrix help

  1. Nov 28, 2009 #1
    1. The problem statement, all variables and given/known data

    Two questions;

    1. Let v1 = [-3, -4] and v2 = [-2, -3]

    Let T: R^2 -> R^2 be the linear transformation satisfying T(v1) = [29, -35] and T(v2) = [22, -26]

    Find the image of the arbitrary vector [x, y]

    T[x,y] = [ _ , _ ]

    2. The cross product of two vectors in R^3 is defined by [a1,a2,a3] x [b1,b2,b3] = [a2b3-a3b2, a3b1-a1b3, a1b2-a2b1]

    Let v = [2,6,-4]

    Find the matrix A of the linear transformation from R^3 to R^3 given by T(x) = v x x.

    A = ? (3x3 matrix)

    3. The attempt at a solution

    For question 1, I found a T[x,y] but it's a 2x2 matrix [{-197, -8/7},{135,8/7}], but maybe i'm understanding the question wrong?

    And for question 2, I really have no idea where to start. Wouldn't I need to be provided with a matrix x if were to find T(x) = v x x? Thanks for any help
     
  2. jcsd
  3. Nov 28, 2009 #2

    LCKurtz

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    You are confusing the representation of the transformation as a matrix with its result as an operator. The domain and range of the operator in 1 is R2. I didn't check your calculations in 1, but if the transformation is represented by the matrix you say it is, you should be able to calculate T([x,y]), which should be in R2.

    You got the matrix in part 1 by knowing what T did to a couple of points in R2. Do the same thing for part 2.
     
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