Math 220 Assignment

September 10, 2001

Assignment for Wednesday, September 12

  1. Let A be the 3 \times 4 matrix

     A  =  
    (
    2 
    3
    1
    -4
    3
    -2
    -1
    5
    5
    1
    0
    1
    		)
    		 .  
    Let f be the function from R^{4} to R^{3} given by f(x) = A x.

    1. Find all points x in R^{4} for which f(x) = 0.

    2. Find all points x in R^{4} for which

       f(x)  =  
      (
      4 
      -1
      3
      		)
      		  .  

    3. Characterize the set of points y in R^{3} for which the relation f(x) = y holds for at least one point x in R^{4}.

  2. Let M be the matrix

     
    (
    1 
    5
    -2
    -2
    4
    -3
    -1
    -3
    1
    		)
    		  , 
    and let g be the function from R^{3} to R^{3} given by g(x) = M x.

    1. Find all points x in R^{3} for which g(x) = 0.

    2. Find all points x in R^{3} for which

       g(x)  =  
      (
      1 
      -5
      3
      		)
      		  .  

    3. Find all points x in R^{3} for which

       g(x)  =  
      (
      -1 
      2
      1
      		)
      		  .  

    4. Characterize the set of points y in R^{3} for which the relation g(x) = y holds for at least one point x in R^{3}.

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