m526_s10_pract_t2_solkey

m526_s10_pract_t2_solkey - ~lATH 5 26 P RACTICE T EST 2 M...

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~lATH 526 PRACTICE TEST 2 MAltCH 15, 2010 [ () 7 -1] 1 1 . pI" 1. (25 points) Let A = 3 is -9 9 ~7 · / O O l [' r o I o \ ! \ 00 I.J _ ,., () {r-l o ~ , () 0 (~ I 0 \ 1 - -_ 0 . . - () - \ -- :? -2 L f o 1',oJ [ 1/ L ~ 6 7 - J, _. = o 0 2 (1)) Usc the L - U - P factorizatioll uf A t.o solve r..:.[ .~~. ~ ~1] [::'.~] = [~~ ]~.t 1.) -9 9 .L':3 33 ,~, L (U)?) ~ f{ ~ --.> r 2 c: r: ,,~ /' r: z: ~~-~ .:> --I - "«'J-+- '- 3 -" / . .:.-;,"';> 2. o () 2 .. _ L)-:~) 1,-. (a) Find the L -- U -- P factorization of A. 3 III 2>(. .... -=-( o . '
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nxm matrix, and b - a nonzero vector. For each of the following answer True or False. (a) The set of all vectors x = [ ~: ] with x, + 3." + 5.'" ~ 0 is a vector space :r l ] (b) The set of all vectors x = :r2 [ ·<:::3 is a vector space. (e) The set of all linear combinations of the columns of A is a vector space. (d) The null space of the matrix A is a vector space. Trl/2
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This note was uploaded on 06/11/2011 for the course MATH 526 taught by Professor Johnson,g during the Spring '08 term at Columbia SC.

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m526_s10_pract_t2_solkey - ~lATH 5 26 P RACTICE T EST 2 M...

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