Math 220 Assignment

November 19, 2001

Due Wednesday, November 21

  1. Find the matrices for change of basis in both directions between the standard basis of R^{3} and the basis formed by the columns of the matrix

     
    (
    2
    4
    2
    -3
    1
    3
    -6
    1
    )
      .  
  2. Let f be the linear function from R^{3} to R^{3} given by f(x) = M x where

     M  =  
    (
    5
    -2
    -2
    4
    -3
    -1
    -3
    1
    )
      .  
    Find the matrix of f relative to the basis of R^{3} given by the columns of the matrix in the preceding exercise.
  3. Let sigma denote reflection in the plane x + y + z = 0 (a linear function from R^{3} to R^{3}). Find the standard matrix of sigma, i.e., the matrix of sigma relative to the standard basis of R^{3}.


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