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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 UFPFlQtR)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 : QZZZL: 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
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why”? WW? W'N/ . Cm > Lg; C Ex; ‘3) «”1 if <;. > ”:3 (C; S) ...
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 Winter '10
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