526pract_fin_s10_solkey

526pract_fin_s10_solkey - M ATH. 526 N UMERICAL L INEAR A...

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MATH. 526 NUMERICAL LINEAR ALGEBRA PRACTICE FINAL EXAM APRIL 23, 2010 Name: There are 8 problems in this test. Show all work. 1. (20 points) Let A = [~ ~ ~] .f< 2 - ~L.R! 3 -2 10 I?i·- ':~I2.J (a) Find the L - U factorization of A. J ;~ l I 'J 2 /) -2 . .. J - I 1 j .~. () ~.' - 1 tl L.\ 1 o /") 2 ') 0 i I (h) Compute the determinants of the matrices L. U, and A.
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([C)l US~ the 3 L]-U ]f A to solve [:);~aCl·toriza[ti~~~O 2 2 8 T2 = 24, 3 -2 10 :r:3 35 L-? .:» /1 r> .- II)' , 1 -, l J 2. -:::'-A ..fr' _ r-. V ~ (""' = II , 2, - /" ' -/-2 ' _ J 1 c: ~ .J _)._ _. • . . J} _. • -'. '0 -2 -( 0 ---) 0 2. 2 g 0 J '') \. () 7 2~r,.1- 2 ~3 -:.: L( -=<) .x'}_= - f 'I ':' -:- "Y'", -I 2> ,), ., -= 10 => 71-::::: '1 i ~ .... ,. ,-9 ei A -;:' ~'/-:t (d) Find the L _ D _ U factorization of A, - ~·t : \"/ ,,' - ,.J , "- I " - L. 0 ! () {] C'J 1 ~~7 °l / 2 0 0 o 1-1 0 rJ 0 2. ~J ~0 - .... ( I
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2] 2. (1.5 points) Let A = 1 3 5 . [ 146 \ I \/) I·~ LI} '"' '..1 [ ., _. ":J (( () /7! 1/) \ . I \ / I ' . l /,")-1 . I . () /) !i ." \ .J I .. J l! /. .~. (b) Use the L -
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526pract_fin_s10_solkey - M ATH. 526 N UMERICAL L INEAR A...

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