Solutions Hmwrk 8

# Solutions Hmwrk 8 - LAST HOMEWORK ME 391 Homework 8...

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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—M-i) + 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 +£3-5a3 ‘ I 2. 0] ‘ ' (27> '5 4* : —-—— .. ‘[- 1-21'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 ‘4-A] 0-0 64%) ‘Ho AL+3A+Z Arm-2 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 44-0 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! CX-Xo)* 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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