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Solution1A - P VL/A c ”T” C:5 c m 2g $69 L\A “T"...

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Unformatted text preview: P VL/A c: ”T”; C (:5? c? m 2g? $69 L \A “T" to MS; CEG/MTH/416/616 “”WWWWWWWWWWM‘ Matrix Computations Quiz 1A . epxeiwsweooam fies 12.} "“9 “"9 Points: 5 points Name (Please Print Clearly): Enter your Quiz number from back: Enter your row number Is this the same number as your ”call out" number you gave as the quizzes were passed out? Circle One: yes no If "no" raise your hand to get the instructor‘s attention. Circle One: CEG 416 CEG 616 MTH 416 MTH 616 CLOSED BOOK, CLOSED NOTES. YOU MAY HAVE ON YOUR DESK YOU’RE YOUR HW 1A COMPLETED ASSIGNMENT. WORK ALL PROBLEMS. MATLAB NOTATION USED. TIME LIMIT 15 MINUTES. 1. (2 points) Let UFP-FlQ-tR)x==0 be the quadratic eigenvalue problem where the three matrices, P,Q,and R, are n by n, write the correct form of the E matrix based on your HW 1A result. The next page shows the relevant expressions from the first and second edition of the Datta text. Only one of the E matrices is correct. 5514 t u at? :Ifi & m "l E n —'P M a? (Q 2. (3 points) For the quadratic eigenvalue problem of problem 1, find all the eigenvalues when n=1 and P =I,Q=:I,R== —I where I==oneby0neidentfiy1nabix. Hint: Set the determinant of the term in parenthesis in problem 1 equal to zero and solve for A values. “WWWW i mt + tlimi“ e11?\ a» awn/’9‘ MM...” 2‘ “\ “1i” E: _ rs» we" \. {‘7' >\, \( >h 1. T‘ L)“ m Hmjirw t. NWNVWMVM 1.. "2.: > 2% Page 1 of 3 Winter 2010 Quiz in Version 1 1“? ME 6: “E“ 1 EE em a .9 not LA. ”1' w M E CEG/MTH/416/616 “““““W**WM Matrix Computations Quiz 1A AW firm lafitem Points: 5 points Name (Please Print Clearly): Enter your Quiz number from back: Enter your row number Is this the same number as your “call out" number you gave as the quizzes were passed out? Circle One: yes no If "no" raise your hand to get the instructor's attention. Circle One: CEG 416 CEG 616 MTH 416 MTH 616 CLOSED BOOK, CLOSED NOTES. YOU MAY HAVE ON YOUR DESK YOU’RE YOUR HW 1A COMPLETED ASSIGNMENT. WORK ALL PROBLEMS. MATLAB NOTATION USED. TIME LIMIT 15 MINUTES. 1. (2 points) Let GER—tfiPntQ)x—-0 be the quadratic eigenvalue problem where the tHree matrices, R, P, and Q, are n by n, write the correct form of the E matrix based on your HW 1A result. The next page shows the relevant expressions from the first and second edition of the Datta text. Only one of the E matrices is correct. : QQéQ i i; t_ 3 n,;‘ J ”a sRQ. VIE: F" 2. (3 points) For the quadratic eigenvalue problem of problem 1, find all the eigenvalues when n=1 and R==—J,F’= —I,Q==I where 1::onebyoneidentwyrnanix. Hint: Set the determinant of the term in parenthesis in problem 1 equal to zero and solve for A values. + 7763 w%:w~>\ “M .. (see )2 f J2; [will 4:3 > if 1 E“ J5 Z n Wng E : QZ-ZZL: 5 " "t : ””’”Z::: Page 1 of 3 winter 2010 Quiz 1A Version 2 The Quadratic Eigenvalue Problem Given the square matrices A,B and C, find scalars l and nonzero vectors x such that (1) (22A+AB+C)x=0 The above is equivalent to (2) Eu==fiu where (3) E==[ 0 I ] First edition of Datta “A“lC —A'IB or (4) E==[ 0 I Second edition of Datta —A‘1B mA—lc In HW 1A you were asked to determine which of the two E matrices is correct. One is correct and one is not. 3M1? am I 3T MMMHMMM LVN—WM; 35;: :5; M M M M ZEMMMMMM%% ‘v% (j “‘¥Kh‘ Y; “JekeM gkw TmésfikMihhwv>g 4T¢W (‘>‘L % s~>\Ci ~¥ ESE):: M Q .£5 E: M ' WW Ti “‘ T R m t!“ a, blots: Mr "3% @Tswfi was (’5‘) b MMMM ( :2 ‘3 MM Wmmi |w~v.M;m.uW.:M_MM:M-M; _. ? -..;.M»M:;v.. M fl.. . a” “09.23: MML-MJMHM‘I rim-$1, «’1‘, Aflg‘vfianu 5” mm MM, M M 1 Page 2 of 3 winter 2010 Quiz 1A Version 1 A paw/«gnw (:fi‘NWw-N fighfiw rfmamfléwfix f if”? \P\ ,‘ L, 1, mix .fi " {:2 , ‘2'." ‘ Ww‘x Q1549 F“ ; "MM a , w :53; Wm: (0 LA (1”an L (3; w as why”? WW? W'N/ . Cm > Lg; C Ex;- ‘3) «”1 if <;. > ”:3 (C; S) ...
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