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pset3 - Problem 7 a Do problem 1 from section 3.3(pg 141 b...

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18.06 Problem Set 3 Due Wednesday, 27 February 2008 at 4 pm in 2-106. Problem 1: Do problem 7 from section 2.7 (pg. 105) in the book. Problem 2: Do problem 10 from section 3.1 (pg. 119). (Give explanations of just a sentence or two.) Problem 3: Consider the system of equations 1 4 2 2 8 5 - 1 - 4 - 2 x 1 x 2 x 3 = b 1 b 2 b 3 a) For which right sides (find a condition on b 1 , b 2 , b 3 ) is this system solvable? b) Call the coefficient matrix A . Is the vector (2 , 5 , - 2) in the column space of A ? How about (1 , 2 , 3)? c) Suppose we add a fourth column (2 , 5 , - 2) to A . How does the column space change? What if we added the column (1 , 2 , 3) instead? Problem 4: Do problem 9 from section 3.2 (pg. 131). Problem 5: Do problem 20 from section 3.2 (pg. 132). Problem 6: Do problem 21 from section 3.2 (pg. 132). (Make sure the matrix you construct has exactly the nullspace asked for in the problem, and no larger.)
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Unformatted text preview: Problem 7: a) Do problem 1 from section 3.3 (pg. 141). b) Do problem 3 in section 3.3 (pg. 141). Problem 8: Do problem 17 in section 3.3 (pg. 143). 1 Problem 9: Define the matrix A = 1 2 2 4 6 1 2 3 6 9 0 0 1 2 3 0 0 1 1 0 a) Reduce A to ordinary echelon form. What are the pivots? What are the free variables? b) Find a special solution for each free variable. (Set the free variable to 1. Set the other variables to 0.) c) By combining the special solutions, describe every solution to Ax = 0. d) What is the rank of A ? Which columns will generate the column space C ( A )? Problem 10: Do problem 4 in section 3.4 (pg. 152). Problem 11: Do problem 21 in section 3.4 (pg. 154). 2...
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