This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 2year 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) AH:  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 Klzéaqyii 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 threedimensional space.
Prove that this triangle is a right triangle. ...
View
Full Document
 Winter '09
 Kouba
 Calculus, Emoticon, University Honor Code

Click to edit the document details