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HW6Math211S11

# HW6Math211S11 - 7 16 17 20(Hint for#20 Try proof by...

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Math 211: Linear Algebra Homework 6 Due April 8 Part I Read Sections 2.2, 2.3, and 3.3 in Leon, and do the following problems: (1) 2.2: 2a, 3df, 4, (2) *2.3: 1c, 2c (3) 3.3: 1de, 2bde, 3(bde), 4bc, 8bc Be sure to provide complete justification in grammatically correct English sentences for both Part I and Part II. Please remember to write Part II on a separate paper than Part I. Part II (1) 2.2: 5, 6, 14 (2) Suppose that A is row equivalent to I and that I can be obtained from A by using only row operations of type I and III. Prove that det( A 2 ) = 1. (3) 3.3:
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Unformatted text preview: 7, 16, 17, 20 (Hint for #20: Try proof by contradiction!) (*) Bonus: Prove that det( EA ) = det( E ) det( A ) for any n × n matrix A and any elementary row operation E , without specifying the type of E in your proof! (Hint: Use induction, and expand det( EA ) across a row that is unaﬀected by E .) * We will not cover section 2.3 in class. There are two algorithms that I want you to have used once just in case you see them in the future, but we will not emphasize them in this class. 1...
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