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Unformatted text preview: LAST HOMEWORK!!!!
ME 391 Homework 8
Assigned: Apr 16, 2008
Due: Apr 23, 2008 Problem 1: Evaluate the determinant of the following matrix using the Cofactor
(5 pts) Expansion. 2  l ~
A: ‘3 2. l
5 o —z_ U615 ZN; Columk because 431C 2’ A:.l(ﬂ‘3i4—7~[ﬂa y’) 4‘ 1+1 7.. ‘l +6 5 5’2 4
Aetvxd—Mi) + 20) =§ 96 Qeum, Coaxch [5 A 5lémJEA Demumaurr
$> 2+5 ‘(S 20% at]. : (i: OCH = " Mil~ Problem 2: Determine the inverse of the following matrix by ﬁrst ﬁnding it’s Adj oint.
(5 pts) A, t Z 3
4 5’ (p
'1 5 lo
«5 :m
Cuzll La :2. Ca: \ 4 U : Z
8 l0 1 to $41A5(Cog“au\1’ : Z Z —3 ‘2‘ if ’3
4 “H a = 2 H L,
' ~3 (a "3 *3 (a 3
A": EA (441 '
, \ Z 3
Ad A ’ Ad’[4 Sb]
1 a 3
5 0 4 b 4t S“
H  Z 4 5
[a 0‘] “1 q] [7 8]
= 2—2. (—2) +3(~3):5 Problem 3: Use Cramer’s Rule to ﬁnd the value of y given that: (5pts) x+y—22=10
2x—y+3z=1
4x+6y+z=2
t l *1 X *0
2 \ 3 W : “\
4 L, \ Z Z
I  (O ‘2— "th‘ﬂLl‘wt— \ “\0 ‘2.
‘3: Z «l 3 *4 o \‘l 'l
4 z \ '[email protected]‘+“y*es o 41. q
\ “'Z —ZK‘+(CZ¢ZZ ‘Z 3‘ ’Z [[‘c‘ 1’} ; Fll" Zcﬂl
*3 11— k“ 4 t, 3 47' q — «\23
«4e +£35a3 ‘ I
2. 0] ‘
' (27>
'5 4* : ——— ..
‘[ 121'l4 3 4 '3
2‘ z ‘4\ M Problem 4a: Determine the Eigenvalues of the following matrix: (5 PtS) 1
3 d! 4 “‘ “H” i i” ’2
a ‘4 A t 3 ‘4A]
00 64%) ‘Ho
AL+3A+Z Arm2 Problem 4b: Determine the Eigenvectors of the previous matrix (5PtS) ‘ ,
A= is l V" “Z
Arr!
_ 2‘423' KI ‘  l 0
PC") ’2— Z L o O 0
5 440 3 ‘5 1254’?” "as
kt’JLL “’1‘
Alf"2‘ I g L z
H—z) 2 '5 “Z o RFRBJ’QZ % 2' O
3«4~6z)/‘*3—20”a 000
3k,sz [all—:2.
um ( i 2' %w 1,}?
 2 l
X .141: ll F—ﬁh “L7,; < 3) iJ’LI:(l)
Problem 5: Use the Taylor Series method to solve the following Inittgll Value Problem.
(5pm) y”—2:E:=o; y(2>=1,y’<2)=0 ‘3: WCrmu
60h: lk I‘M: “:1 I . m
(23 (C2) _ (Z) 2 g (2)
(9 "25(1)‘ 0! * at! CXXo)* 3370(4) “L 3‘.
(WM give/How‘ auqs 2X9] ’
m If 2x
8(4) l a U
a (X 3 FZXZB
guhshb’i‘ﬁ X12. 8 ocah‘m {Age “(zlazCD LAMA =L gmtal: 13:2: 2(2) ‘ 34203 14(0):;
“3 ’ t 332(1)" 1‘ 0+ 10:9
6 (AAW 5%?) 4t) 4C _L_ 505 [MID (D
I ,L 2 4
aclchCX’Z) *‘306‘2334’ 3 CV2» +2.. ...
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 Spring '08
 BLAZERADAMS
 Mechanical Engineering, Following, 4 L, 2 g, 3 W, 5pts, 2 L

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