Practice Exam with Solution for Linear Algebra | MATH 203, Exams of Linear Algebra

Material Type: Exam; Professor: Kiley; Class: Linear Algebra; Subject: Mathematics; University: George Mason University; Term: Fall 2010;

Typology: Exams

2010/2011

Uploaded on 07/20/2011

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3 Exam#2
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 |
lz 3
lo '9
I;,"1
3 s[*
| 0t
ECK
?
4
c
or-verheequarion. *_ ISI i ,'
A^rln; Ll.f ; il|= l;l ] 1l -, ,
,t3[ - 11 -3, ;i f I, l: -i t'* ;{,1
ItltLooat Il Io ct z 2 i' t
4r = 5/f *z/y*r-?&?q;4s= ,U1*:
:
: wl = .f il' | ;}, ^f*'^VA[='; +
L''tl L'rLr
I
1,1= [" ', ;l
r).A=m @rr/r"d
OS
I
t.
_5
,{4
v
)
t
3
1
:l
t
:l
t-
t
5/8
Y7
'ilt
D
-{,
I
.,,
/g
'li
it
5
factori zation
1 5lx: I
gr_ven
U
4-3
00
,'I
t4,
tl
ztl
o
tsl-.a
tl
tl
3
?
0 0 0l
"7 0 0l
6 -7 0l
3 8 2l
.rr- 1't/
n- o\'/(-
,.
2 3 |
t:?
o 7/{
t 31,
V/r1
lt l.tu
L3)
+42
I
e
I
a) Find det A.
b) Find the eigenvalues of A.
n\ Tq A in\Tar1-ihle" F',xnlain-
vt r u::yrsrrr.
Z
5
-3
4
?,7t'
/, 7 ! U/'/d''/ slrea )
ll e3 sl- rt a
lo-r'/ol'L(7 L=L= '-
ES lhra"a//A* o
Math 2
W. T.
Answer
I.o -L -L OW
B\''
$) 2. Use
L
110
121
l
/a),; =
"+'
<)
1)
pf3

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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 (^) |

lz

I;,"1^ lo^ '

3 s[*

| 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

il' |^

;}, ^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-

t 5/

Y

'ilt

D -{,

I

/g

'li

it

5

factori zation

1 5lx: (^) I

gr_ven U 4- 00

,'I

t4,

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,

V/r

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

  • 4

?,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''

$)

  1. Use L 110 121

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

(s

are bases for^ Rt. C are l-3 2)'^.

J*z- 9aY

?rfq)dErQ

b) Col A; c) Row A.

41'3t-

r U41 =q ' 7'b-34+:a

-f45:g

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 .\

af=^0

Is

', (^) lo 100

J,=

4

hrr;

,!

sl

  • (^) S/z

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

ri

tr-

I

l

OL^ -+ at

I J

d oo Ld aa^ t-

I

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an

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9'

7

tt l 'ros :es -es

,l I I

t'

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w nat a tta L

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{ t I the I the I the

zf

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L

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I

[9) s.

" a) b)


a,)

0l', (^) t vector coordi coordi

tl+

IJ

| 1--

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B ta ta ta

, (^) , 3l*l

0-25) [o

I

4l"I=r:l

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r\

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[-^ r/z^ \

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