Mth510TestSolutions_W05

Mth510TestSolutions_W05 - 1 RYERSON UNIVERSITY DEPARTMENT...

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Unformatted text preview: 1 RYERSON UNIVERSITY DEPARTMENT OF MATHEMATICS MTH510 MIDTERM TEST February 17, 2005 Part A: Short Answer 1. Let A = - 1 3 4 3 4 2 2 1 , P = 1 1 1 , and B = - 3 1 (a) Find the LU factorization of P A showing all steps. L = 1 2 1 1 1 , U = 2 2 1- 1 2 1 (b) Use the factorization in (1a) to solve AX = B . First solve LY = P B to get that Y = 1- 2- 1 and then solve UX = Y to get X = 1- 1 , which is the solution of the original equation. 2. Find all three roots, x 1 , x 2 and x 3 , of P ( x ) = x 3- . 1323 x + 0 . 018522 to 6 significant digits. Show your work in the space below, but record your final answer, here. x 1 =- . 42 x 2 = 0 . 21 x 3 = 0 . 21 3. (a) Write down the third degree Taylor polynomial, P 3 ( x ) for 3 √ 1- x expanded about the point x = 0....
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This note was uploaded on 05/19/2010 for the course MATH MTH510 taught by Professor Kolasa during the Winter '05 term at Ryerson.

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Mth510TestSolutions_W05 - 1 RYERSON UNIVERSITY DEPARTMENT...

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