108AQuiz3 - Name: WW.- Mathematics 108A: Quiz 3 Friday. May...

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Unformatted text preview: Name: WW.- Mathematics 108A: Quiz 3 Friday. May 28, 2010 Professo: .1 Douglas Moore Part L flue-False. Cii‘cle the best answei to each of the following questions. Each question is weith 2 points 1.. The set Z4 2 {G,1,2,3}, with the opeiations of addition and multiplication modulo four is a field with finitely many elements 2 If W} = {($1.12,$3)€ R3 : :3; + 232 — 3563 u G}, and W; = Span(1,1,1), then R3 is the déiect sum of Wl and W? Venue 3‘ Let ,6 = (vhvz) be the basis for R2 defined by we me- If T : R2 —+ R2 is a, linea: map such that T(v1) = 3v1 and T(v2) 2 7w, then the matzix of T with respect to 6 is mg = (3 3) @ FALSE 4. An element A E MnxnUF) is invertible if and only if it is a. pIociuet of elementary matIicesr TRU FALSE 5. Let W be the subspace of R4 defined by W =span((1,2,{),5),(0,0,1,4}) if H” is the orthogonal complement of W, then ((1, 2, 0. 5), (0, 0. 1, 4}) is a basis for WJ“ Part IL Give complete proofs of each of the foliowing statements 1‘ (5 points) Find the inverse of the matxix OWOG ‘ i 0 E0 5 ‘3’ “my E C?» M: F a :3- 6) {3 i y {if} “7 35 if} 0 i {00%4’“3‘”’ too thaw l I€D{“Il<‘3 Wm mica—«f it}! a } if) 6,) 2 o (,3 E (3 Ci? 3 4- “3 a: - “'1 .2: ; I a) a C} 0 ~31 2 (5 points) Find the determinant of the matrix 2 1 O O l 2 1 0 ‘4‘ 0 1 2 1 0 0 1 2 (Hint: it is easiest to use elementary 20w operations ) I I “L E 100% MQGQE llocla‘ 1&0?m9‘512.3‘31-m‘20%~1@' E. ” i *- In 1 J” O U l w {:3 :3 l I a" h ? ; 3 2+ ) J E 3 0 3 i3- 2 s L 3‘3; 0 l s 9 a E *2. l o 0 I} O 5:" {3 'E ‘3’ 'D’ I 3" O o "y I 1L C: L” «a l 2‘ \I 0 : 0'§Q «* O I 3’1 i “5" w. E‘ ‘ ' C) (D I ‘f E O 0 “if 2 U; Q 0 ‘ a» 0 a gig" ...
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This note was uploaded on 06/05/2010 for the course MATH Math 108a taught by Professor Moore during the Spring '10 term at UCSB.

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108AQuiz3 - Name: WW.- Mathematics 108A: Quiz 3 Friday. May...

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