Math 220 Assignment

October 5, 2001

Due Monday, October 8

  1. Find the inverse of the matrix

     
    (
    1 
    2
    -4
    1
    -2
    10
    -1
    1
    1
    0
    1
    5
    2
    -9
    1
    0
    		)
    		  .

  2. Let f be the linear map from R^{4} to R^{4} that is given by the matrix

     
    (
    1 
    2
    -4
    7
    -2
    -1
    -1
    -8
    -1
    4
    -14
    5
    5
    7
    -11
    29
    		)
    		  .
    In this example it will be observed that the reduced row echelon form of the matrix M has only two non-zero rows. We shall come to understand that in this situation both the kernel of f and the image of f are 2-dimensional. Some who teach linear algebra regard this scene as a pons asinorum.

    1. Obtain a parametric representation for the kernel of f.

    2. Find a pair of equations in 4 variables that characterize the image of f.

    3. List a pair of equations in 4 variables that characterize the kernel of f.

    4. Give a parametric representation for the image of f.

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