Homework 6 Due Thursday, March 7, at the beginning of class

You may do the calculations necessary for these problems either by hand or with Maple. Please submit a handwritten solution, or email an ASCII/Postscript/html document to the TA.

• Textbook, Chapter 3, Section 2, p. 129, Problem 19.
• Textbook, Chapter 3, Section 4, p. 148, Problem 9.
• Consider the following matrices:

                             [ 17   1  -13  -15  -14 ]
                             [                       ]
                             [  4  -1   -4   -1   -1 ]
                             [                       ]
                    A :=     [  2   1   -6   9    7  ]
                             [                       ]
                             [ -4  -2   3    4    4  ]
                             [                       ]
                             [ -3  -3   4    -1   0  ]
  
                                         [  -4 ]
                                         [     ]
                                         [  -9 ]
                                         [     ]
                                    b := [ -25 ]
                                         [     ]
                                         [  -3 ]
                                         [     ]
                                         [  5  ]
  

  Using the column echelon form algorithm discussed in class (on March 5), find a single solution to Ax = b and a basis for the nullspace of A. Here is the Maple program generating this example.

The head of the math department has authorized extra "drill" exercises to be checked by Michael McLean for no credit. These exercises are intended for those who have difficulty with the concepts. Michael will tell you if you have done them correctly and help you if you have difficulties getting them right.

• Textbook, Chapter 3, Section 2, p. 128, Problem 11.
• Textbook, Chapter 3, Section 3, p. 140, Problem 5.
• Textbook, Chapter 3, Section 3, p. 141, Problem 16.
• Textbook, Chapter 3, Section 4, p. 148, Problem 13.