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MAT444test2-09

MAT444test2-09 - MAT 442 Test 2 Instructor J Jones Name 1 2...

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MAT 442: Test 2 Name: Instructor: J. Jones 1 2 3 4 5 6 Total 12 pts. 22 pts. 18 pts. 15 pts. 20 pts. 16 pts. 103 pts. Write your answers on separate paper. Make sure your name is above and on every sheet. If a problem asks you to prove a result already covered in the course (Theorem, example, or exercise), you need to prove it here. You may use a calculator for this test, although it is unlikely to help. Throughout, F is a field. 1. (12 points) Read these instructions carefully. For each type of row operation give the following: (a) A description of what it does (so we know which row operation you are talking about) (b) The determinant of a corresponding elementary matrix E (c) State whether or not E t is an elementary matrix (d) State whether or not E is invertible, and how we know that. Note, you do not have to know the number which goes which each type of row operation, but you have to cover all types. 2. For each part, state the definition or theorem for linear operators.
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