This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Name: WW. Mathematics 108A: Quiz 3
Friday. May 28, 2010
Professo: .1 Douglas Moore Part L ﬂueFalse. 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‘31m‘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" ...
View
Full
Document
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.
 Spring '10
 MOORE
 Linear Algebra, Algebra

Click to edit the document details