Math 220 Assignment

November 26, 2001

Due Wednesday, November 28

  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

     
    (
    3 
    6
    2
    2
    -3
    6
    6
    -2
    -3
    		)
    		  .  

  2. Let f be the linear function from R^{3} to R^{3} that has the matrix

     D  =  
    (
    2 
    0
    0
    0
    1
    0
    0
    0
    3
    		)
    		 
    relative to the basis of R^{3} given by the columns of the matrix in the previous exercise.

    1. How many lines L passing through the origin have the properly that f carries each point of L to a point of L ?

    2. Find all points x in R^{3} for which f(x) = x.

    3. For each of two different lines through the origin find a point on the line that is carried to another point on the same line.

  3. Find the matrix of one of the two rotations through the angle pi/2 about the axis in R^{3} containing the origin and the point (1, 1, 1).

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