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homework2-1 - Math 20F Lecture C(Winter 2008 Homework 2(Due...

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Math 20F - Lecture C (Winter 2008) Homework 2 (Due on Wednesday, February 13th by 3pm) *Please drop your homework into the homework box on the 6th floor in the APM building. *This homework covers sections 2.1-3 and 2.5 from your textbook. *You don’t need to turn in the questions with (*). But I highly recommend to solve these questions as well. These are proof questions. Working on them should give you insight about some most fundamental concepts that we couldn’t touch on in class. Sometimes these exercises will let you make connections between seemingly unrelated topics. 1. (Section 2.1) Solve questions 2.1.2, 2.1.6 and (*) 2.1.25 from your textbook. 2. (Section 2.1) Let A = [ a 1 a 2 ...a n ] = ¯ a 1 ¯ a 2 . . . ¯ a n and R n = 0 0 ... 0 1 0 0 1 0 0 1 0 0 1 0 ... 0 0 . be n × n matrices. Express the products AR n and R n A in terms of the columns ( a 1 ,a 2 ,...,a n ) of A and rows (¯ a 1 , ¯ a 2 ,..., ¯ a n ) of A , respectively.
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