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Unformatted text preview: MAS 3105 May 18, 2006 Quiz II and Key Prof. S. Hudson Suppose you are asked to find the inverse of a 2x2 matrix A , which appears below. And I do most of the calculation for you: [ A | I ] = 1 1 1- 2- 1 1 → 1 1 1 1 2 1 → 1- 1 ? 1 2 1 1) A is the first two columns of the first matrix. What is A- 1 ? Check your answer. 2) The first “ → ” is a G.E. step. Find the elementary matrix E 1 that does that step. Then find E- 1 1 . 3) Express A- 1 as a product of elementary matrices. (Write them out, in order). 4) You can use this calculation to get an LU factorization of A . What is L ? [hint: use part 2] What is U ? Check that A = LU . 5) [20 pts) Choose ONE of these to prove, on the back. Use words and sentences and standard methods to completely explain your reasoning and your formulas. a) If A and B are symmetric and AB = BA , then AB is symmetric. b) If A is nonsingular then det(A) is nonzero....
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This note was uploaded on 12/26/2011 for the course MAS 3105 taught by Professor Julianedwards during the Spring '09 term at FIU.
- Spring '09