exam3sol 17B

exam3sol 17B - Math 17B Kouba Exam 3 KEY Your Name :

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Unformatted text preview: Math 17B Kouba Exam 3 KEY Your Name : _______________________________________________________ __ Your EXAM ID Number ____________ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE T O, IN ANY WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most cases, a correct answer with no supporting work will receive LITTLE or NO credit. What you write down and how you write it are the most important means of your getting a good score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page. 6. You have until 10:50 a.m. to finish the exam. 0 2.3 1.8 1.2 0.1 0 0 0 0 0.4 O 0 0 O 0.6 O a.) How many age classes are in this population ? @ b.) Wha - - ntage of 1—year old females survive to the end of the following breeding season ? c.) What ercenatge of 2—year old females survive to the end of the following breeding season ? d.) What is an average number of female offspring for a 0-year old female ? @ e.) What is an average number of female offspring for a 3—year old female ? ® 1.) (3 pts. each) Consider the Leslie matrix L z 30 f.) IfN(0): ,determine N(1). 40 "o 4.3 (.3 (-2 '3’0 ‘23+3e+43 1:7 (0 3 _ o.( O O o z : N0)” 0 0.44 o 0 3° 4 ‘4 O c 0.6 o ‘fO IX (.2 2.) (8 pts.) Use matrix reduction to solve the System { :x+_yy::2_l . l l 2 l l l 1 l 2 3 ‘1 ’1 0 "q ‘7 N o l 7/<{ l ( o /4 _ i __ 1 [a ( 7/4, l "—5 X‘ LI] «7 ‘ ’~/ 3.) Determine the inverse for each matrix. a.) (6 pts.) A '5 “‘l \ a? O O ( 3—1 2 0 ‘o—(IOO 0(0010 "((000( [o-( No\0 oo*l Loo Noio ool ) 4.) (8 pts.) Find an equation of the line in parametric form passing through the points (—1,2,0) and (0,3,—4) . . ‘o-el) l WWV=[3~9\]:[(} a ~q~o “‘1 x: “(4—‘{: L." y: 72¢{r £1 O—q‘e 45/? fem 3 —4 x. Y (1}(6/+(~Aj(~3j+(3j6‘f2 - (xHY/ V (02463236qu ——~—-———-— 20 ———» 9:?OC’H “\llq'vél Tr, . 1W 1 6 5.) (8 pts.) Determine the angle 9 between the vectors (-2) and (—3) . MS: 6.) (10 pts.) The given 2x2 matrix is a Leslie matrix. Determine a stable age distribution for this matrix. Is the population increasing or decreasing in size ? “(:34 3) MCAv-AI]: M[Q")‘ jg] Fm Al:3 - W CA-Al/X3G —’ _ n .. o “Xi‘LqXRIOM M x&;-é Mafia ——» x,:<4><&:<H__ 4,, X_ [my 4e]~%[HZ 7W MM ‘1 X; ‘E h I j . ‘ . ‘9‘? 7-) (10 pts.) Find eigenvalues and the corresponding eigenvectors for the matrix —2 5 __ ~ , AZ<4 6) MCA—AI): M[ZA 631] = GQ~AlCévUvCé7C40 "v Al~ex+ax—t2~xo " AX~q/\-3oZ-: CA~3_)(5\+4()::0 a /\:5’J A:~<{ :02 A58" [132;:i~[;:2{:i~ut:a/:i—a 1 _ -1 AL XI~EXQIO MMX‘RJV‘E’ XI'EK&'&L) \— 8.) (8 pts.) Determine an equation of the plane which passes through the point (2,0, —1) and which is parallel to the plane 2 = 3m — 4y + 5. (OX: (07/0/‘4/J 2:.- 3x~qy+€~> sx— 4Y~% : ~b’ Aw Mil W12 W 44‘ 3(x~2j~q(y~o/« <g+i]: o 9.) (8 pts.) Give an example of a 2x2 rotation matrix which rotates vectors 60° clockwise. W [M6 "We 0 0 10.) (6 pts.) Assume that A is a 2x2 matrix. If A2 = (O 0 >, must it follow that A = <0 0) ? If this statement is true, explain why. If this statement is false, find an O 0 example for which A 75 PM/ we A:[§o‘], The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. ’1.) Determine the 2x2 matrix which has the following eigenvalue / eigenvector combinations: A1 = 2,V1 = and A2 : —3,V2 = W I l q+hz 1 [Sillilfilltla 5cm: x a “l t41=c~sal‘:1-—>l::::3:i MAL 25M (“—1 (3 9.. J Earl-(OZA ai’gbzs'a b: 573 M a:(/3 ~4+aht3 C+Ol29\ de-qa dz‘ioMQqJfi {mauve—7’ 3 3 A: V3 “73 "9/3 5 a ...
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This note was uploaded on 11/26/2010 for the course MAT Mat 017B taught by Professor Kouba during the Winter '09 term at UC Davis.

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exam3sol 17B - Math 17B Kouba Exam 3 KEY Your Name :

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