BlueMidterm - 8er Exam Midterm Exam Math 2.] November 2,...

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Unformatted text preview: 8er Exam Midterm Exam Math 2.] November 2, 2007 Instructions: You have 50 minutes to complete this exam. All relevent work must be shown to receive full credit for a problem. N 0 credit will be given for illegible solutions. Name: Problem 1: (25 points) Determine the solutions (if any) to the following system: 1:1 + 23:2 + (£3 — 2x4 2 1 211+ 12:;- :133+ 33420 + 3:2 — film-3 + 2174 :1 5.171 + 1:2 — 411-; + 5234 = 2 Problem 2: a): (5 points) If E is the elementary matrix 100 E2010, 021 describe the effect of multiplying a matrix A with 3 rows by E on the left side (in other words, how is EA related to A? ) . Snag Eis Ohlbtmeo‘ {tom 1:? re lacin line, % VOMJCTLB by Hrs 5077? M141 wines +lxe Se ml FEM) A "5 H16 modifix olDl'm'nBfil xii? : tieléglééai RM Ofl A by #5 sum Mfr/7 6141M 10! .l 1t 00 J MM (1-. CalCUifllQ odi’JC/Sll iifil T‘QK \‘ at ‘l W AlA A n 7H6le lernJr on Awidl A A) I A“: @1240? [ail/Agfll’tl lR 12L b): (20 points) If A is the matrix flfihvlli li—l (00 1214100 132\[email protected]@i$m[0L Elna 3.6;? 001 00!, 00100t@~9@[email protected] Hiemgloo 3177 - (LE/.3 (NOR—1V3 so Kl: «ax 3?: ool OO\, ’ 001 LaoK fir Niall ‘llxa Corrh 71' C (see exercise (-6 trth 0 A; j: "1 Cl] “l 1 C4. OOl $6” Ill-4AZI’3 W‘di Qt?) Cat—3' Problem 3: (25 points) If A is an n X n matrix satisfying A2 = A, show that either A is In or A is Singular. SibflLflQL Whoa/i (60+ IszL/LYEQ awa/(JMEPSMMW 0! (9mg: We are giVerW A 7A WE; magi Cashier 14xe MSiéiiii‘y #955 A 6; MASMflulCLF) $0 ififirais‘a MNX Wan/“2M jaw/is; WWW AEA by A“ (m +Ae, (3% W} 4v (72% A-lAZ :A-I A :9 [PM = AW :2) i A :31 W3C A “W A (3/516? Haw (but Me QE is 35 CWft/Sin W? MAT; defCA‘ir—dZdW’ (OHM: d A6094: or @64in Q i d mi) 1 w . w "l M" 9: Aiwsiw Aafme. Problem 4: Let A be the 3 X 3 matrix a): (5 points) a 2 0 A = 3 1 O . 5 3 2 If tr(A) = 7, find det(A). «EFUQ Hie. sum down He {min 0&3 oral: {:rCA\= 0L+K+7\:;Z:;>q/—_4{— ‘é n COILWW - 1 b): (20 points) Find the eigenvalues and all corresponding eigenvectors of the matrix A = [i "1]- 12) (wt (Hayes) may 43 (A—mco \ 1% ~\ + :9 (a-MCMH \eO EAKVéXm—JO [My one make ewe—:0 <> x23 72 m [:32 [1‘ “SIN m, 2E] :9 Augmefiféfll “0+?” 3 “3W [3; {if} v karma SQ “XItXAE—OQX\:~9< if Sowflons? g“ [1)]: 0(6) J ...
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This note was uploaded on 03/11/2012 for the course MATH 2J 44360 taught by Professor Donaldson,neil during the Spring '10 term at UC Irvine.

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BlueMidterm - 8er Exam Midterm Exam Math 2.] November 2,...

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