

Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Material Type: Exam; Professor: Kiley; Class: Linear Algebra; Subject: Mathematics; University: George Mason University; Term: Fall 2010;
Typology: Exams
1 / 3
This page cannot be seen from the preview
Don't miss anything!


3 Exam#
iley November^ 23,^ 2OlO
in the space provided.^ Give^ cl-ear^ explanations.- the Honor Code.^ No^ books,^ notes,^ or^ calcufators^ aflowed.
an LU factorization for (^) | 2 3 5 (^) |
I;,"1^ lo^ '
| 0t
ECK
?
c
or-verheequarion. *_ (^) ISI i
,'
A^rln;
Ll.f ; il|=^ l;l^ ]
1l
-, ,
,t3[ -^11
-3,
;i f^ I, l:
-i t'* (^) ;{, ItltLooat
Il (^) Io ct^ z^2 i'
t
4r =^ 5/f^
z/yr-?&?q;4s= ,U1*:
::
wl
=
.f
;}, ^f*'^VA[=';
L''tl
L'rLr
I
1,1= (^) ["
', ;l
r).A=m @rr/r"d
OS
I t.
_ ,{ v
t
3 1
:l
t :l
t 5/
Y
'ilt
D -{,
I
'li
it
5
factori zation
1 5lx: (^) I
gr_ven U 4- 00
,'I
tl
ztl
o
tsl-.a
tl tl
?
0 0 0l "7 (^0) 0l (^6) -7 0l 3 8 2l .rr- 1't/ ,.^ n-^ o'/(-
t:?
o 7/{
t 31,
lt l.tu
L3)
I
e
I
a) Find det^ A. b) Find the eigenvalues of A. n\vt Tq A in\Tar1-ihle" (^) r F',xnlain-u::yrsrrr.
Z 5
?,7t' /,^7! U/'/d''/^
slrea (^) )
ll e3 sl-^
rt (^) a
lo-r'/ol'L(
L=L= '-
ES lhra"a//A*^
o
Math 2
W. T.
Answer I.o (^) -L -L OW
B''
$)
l
/a),; (^) =
"+'
<)
rJ 5- -3 I 05 00
andB=
*xJ 1-3 0 002 000 000
1-3 4-r 9 -2 6 -6 -1 - -3 9-6-6^ - 3-9 4 9 0
(r) n. are row equivalent.
(r
are bases for^ Rt. C are l-3 2)'^.
J*z- 9aY
?rfq)dErQ
b) Col A; c) Row A.
r U41 =q ' 7'b-34+:a
r,4( (^) /e
CH cK^ ALE^ I^ o^
oO (^) AFs o^ +
t-2-3 L+^
-b -^ 4,
-/0 ' 3'
til=4xr4(y(6),%
-7 0 5 -'l^0 e'3'J" 00
iaa .\
Is
', (^) lo 100
4
,!
sl
t-1 11r (^) f t1L' -'llr} t tes rel-ative to to C of l-3 2)'. t (^) ^€ -v!IL t-1.r^ L)t1,
I
-l
1 I iina .ve rve
(. rd
tr-
I
OL^ -+ at
I J
d oo Ld aa^ t-
I
1l wh -!dL ^+
an
) rg ;re f-r I I
9'
7
tt l 'ros :es -es
,l I I
t'
L
w nat a tta L
-) (-
{ t I the I the I the
zf
L
'l
I
" a) b)
a,)
0l', (^) t vector coordi coordi
tl+
IJ
| 1--
_,w fJ
B ta ta ta
, (^) , 3l*l
I
4l"I=r:l
','l-f
/r
, I l?- K_Tb
r\
[-^ r/z^ \
-5 (^) 0, (^) e | (^) 01,,
C}+EC
o