# pset2 - 18.06 Problem Set 2 Due Wednesday, 20 February 2008...

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Unformatted text preview: 18.06 Problem Set 2 Due Wednesday, 20 February 2008 at 4 pm in 2-106. Problem 1: a) Do problem 5 from section 2.4 (pg. 65) in the book. b) Do problem 26 in section 2.4 (pg. 69). Problem 2: Do problem 24 from section 2.4 (pg. 68). Problem 3: Do problem 7 from section 2.5 (pg. 79). Problem 4: Define the matrix 1 2 -4 A = -1 -1 5 2 7 -3 Using elimination one can calculate that the inverse is -16 -11 3 5 1 -2 A-1 = 7 2 2 5 3 1 -2 -2 2 a) Suppose that we formed B by switching the top two rows of A. What would B be? b) Now suppose we defined C by adding three times column(3) of A to column(2). What is C -1 ? -1 Problem 5: Do problem 23 from section 2.5 (pg. 80). Problem 6: Do problem 29 from section 2.5 (pg. 81). As with any True/False question, be sure to explain your reasoning: give a brief proof if the statement is true, and give a counterexample if the statement is false. Problem 7: Do problem 12 from section 2.6 (pg. 92). 1 Problem 8: Do problem 13 in section 2.6 (pg. 93). Problem 9: Do problem 28 in section 2.6 (pg. 95). Problem 10: In this problem we will forget to include your code! Define the 2 -1 A= 0 0 use Matlab to do LU factorizations. Don't matrix -1 0 0 2 -1 0 -1 2 -1 0 -1 2 The command [L,U]=lu(A) will decompose A into L and U . We can further decompose U by using the fact that A is symmetric, so that U = DL (the ' denotes transpose in Matlab). What are L, D, U ? What will the pattern be for larger matrices of the same form? Now, factor B = [1,2;2,5] into B = C C by using C = chol(B) (here chol stands for Cholesky). Try using the command [L,U]=lu(B). What happens and why? We'll need to include a permutation matrix P via the command [L,U,P]=lu(B). Find L, U, P and check that P B = LU . 2 ...
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## This note was uploaded on 08/10/2008 for the course MATH 250 taught by Professor Chanillo during the Spring '08 term at Rutgers.

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pset2 - 18.06 Problem Set 2 Due Wednesday, 20 February 2008...

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