mt2 key

# Mt2 key - Midterm 2 Math 20F Lin Winter 2010 Place all books calculators and papers under your desk You may have a 4 x 6" handwritten note card

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Unformatted text preview: Midterm 2 Math 20F Lin Winter 2010 Place all books, calculators, and papers under your desk. You may have a 4 x 6" handwritten note card . On the cover of your blue book write your name, student ID number, section time, and color of your exam. In a column number one to four. Show all your work, and box your answers. You must give correct reasons for each answer to obtain full credit. Good luck. 20 ~01) 1. Let A = 1 A has eigenvalues 1 and 3. ( -1 0 2 (a) 18 pts. Find a diagonal matrix D and an orthogonal matrix P such that A = PDp T (b) 4 pts. Compute A4 by using part (b) . (c) 10 pts. Write A = )'1 uj uj T + .A2"U2U2T + .A3UJU-:/ for orthonormal vectors U-I, U2, uJ 2. Let T : \R 2 -> \R 2 be the linear transformation defined by T G~) = C~: =: ~~2). (a) 3 pts. Find a matrix A such that Ti = Ai. (b) 10 pts. Let B = {b~,b~} be the basis b~ = G) b~ = G)' Find the B matrix for the linear transformation T . (c) 7 pts. Let i = G) . Compute IAxls . 3, (a) 18 pte, L,t A ~ G D' Find th, QR lactmi,.tio, of A. (b) 10 pts. Find the least squares solution to the system of equations X2 = 1 3XI + X 2 = 4 6XI + X2 = 5 (0) 10 pt" L,t n, ~...
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## This note was uploaded on 04/21/2010 for the course ECON x taught by Professor Xie during the Spring '10 term at UCSD.

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Mt2 key - Midterm 2 Math 20F Lin Winter 2010 Place all books calculators and papers under your desk You may have a 4 x 6" handwritten note card

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