pracexam3sol 17B - Math 17B Kouba Exam 3 Your EXAM ID...

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Unformatted text preview: Math 17B Kouba Exam 3 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 TO, 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. N 0 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 6 pages, including the cover page. 6. You have until 10:50 am. to finish the exam. 1.2 1.5 1.1 0.6 . . . 0.9 0 O 0 1.) (3 pts. each) Conmder the Leshe matrix L — 0 0'8 0 0 0 00.70 a.) How many age classes are in this population ? Ll b.) What percentage of 2-year old females survive to the end of the following breeding season ? ‘7 o 670 c.) What percenatge of 3—year old females survive to the end of the following breeding season ? O 672) d.) What is an average number of female offspring for a 0—year old female ? l ' '71 e.) What is an average number of female offspring for a 1—year old female 7 l . f 10 f.) If N(O) = ,determine N(1) . 30 r [.1 [.5’ |.( 0.6 ‘0 “19304—4444le loq _. o N (ll ~ 0.1 0 o o 9‘ 1 c‘ 1 ‘l ' 2 8 a 2.) (10 pts.) Use matrix reduction to solve the system { gy__yz+:3: 1 t-/ .(l l"l I l] l02~1l3l~l0 l "43/1 [ O [/4 ‘57:,~ EX+§£ZC 52K N [O ( "l/x 1 O l 3.) (10 pts.) Determine the inverse for matrix A = ( 2 —1 0 ) ( o l l O o i O 0 “9/5 3//0 V10 0 t 9‘ & ~L 0 ,U 0 x o 4/6/ “2/; (/5’ O 0 I 3/5’ "3/(0 #I/IO O o i 3/5 — (o ~4/10 4.) (10 pts.) Determine the point of intersection of the plane 33: ~ y + z = 5 and the line so = t + 1 given parametrically by L : { y = 1 — t .. z=t 3><~y+ 2:5 P» (Sag/,4 3&+,/_O~H+ (#:5r ——-? 3f+3~f+f+~‘é 26' .4 5++02:5-—» 5’79:E——»Jc=%—22eb« X13/5’4’l: 67/” 7’: («B/5’33/5‘ Z: 3/5’ -1 2 5.) (10 pts.) Determine the angle 6 between the vectors < 1 ) and < O ) . -—! M A: W 0 W3 A’Q __ —-;L+0+° Q1+{+O\M+o+q .. ~°2 -— EZ’réL “'4 . {El/'57 W; V 7 6 e : 2;”: 3 6.) (10 pts.) The given 2x2 matrix is a Leslie matrix. It’s eigenvalues are 3 and -1. Determine a stable age distribution for this matrix. Is the population increasing or decreasing in size ? g 2 6 _ a~A G; A“(1/20) A-H: - 1/; M) 7.) (14 pts.) Find eigenvalues and the corresponding eigenvectors for the matrix A ~ 2 2 ‘ — 2 —1 amulnza**** dflkfi*fl# ‘ 9c ~(~/\ : A"+x\—5{A—.2 ~<¥ : A"~—A~é : (A~3/Q+2/:o _. A;3/ ,\:-,2 , 71mm (A~,\_t)7<:o: I l 2. , ——r 1 o {—2 0 Al:3 ' [L—q OIV[O ofozfi Xl—RXJVZO I: MM Klz-é-aqyii A x ><={x2]=[°?f :+[fi3%¢m WHY; X, Xi ~21 ififl~lzffigh X‘+3L~XJ~:O 'a’ M X9319 Vfig K‘:~;:—‘6 40 X: £5.41 [‘i*l=i+[1‘lao W V0131] 8.) (10 pts.) Determine an equation of the plane which passes through the point (—1, 0,2) .7: = 2 —- t and which is perpendicular to the line given parametrically by L : { y = t + 3 . z=2t __\_ W N: ~( 9.) (8 pts.) Determine if the following 2x2 matrix is a rotation matrix. If so, determine the angle and direction of rotation. R—(1/2 ~\/§/2) ~ We "we, * \/§/2 1/2 ‘ Me 0049 (l The following EXTRA CREDIT problem is OPTIONAL. It is worth 10 points. 1.) The points (0, O, 0), (1,2, —1), and (3, —1, 1) form a triangle in three-dimensional space. Prove that this triangle is a right triangle. ...
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