Applied Math 1411b Assignment 5
DEADLINE 9:30 AM, UCC 146, FRIDAY FEBRUARY 11
* Problems are to be handed in at the beginning of class in UCC 146 on Friday February
11. Or they can be handed in at the TA Oce Hour on Thursday February 10, 3:30  4:30
pm, a
1
THE UNIVERSITY OF WESTERN ONTARIO Department of Applied Mathematics London Ontario Applied Mathematics 025b Second Tutorial Test February 21, 2008 60 min
Name: Solution
Section 2
Closed book. Only simple calculators are allowed. Print your name above an
1
THE UNIVERSITY OF WESTERN ONTARIO Department of Applied Mathematics London Ontario Applied Mathematics 025b First Tutorial Test January 31, 2008 60 min Name: Solution Section 2
(1) Closed book. Only simple calculators are allowed. Print your name above
A t some level this course is about
vector spaces V
T ypical Exam Question from 4.1:
Consider set of nXm mt rices abbreviated M nm possible Q involves demonstrating that M nm is
a vector space this question is too long for a test
BUT
You can expect instea
Cross product of two vecotrs.
4.1: Vector Spaces
Simplest models are linear models.
Always look early: is there a zero vector.
Here obvious candidate:
Demonstrate this is ok.
Omit p. 139140
EX> Formulate equation of a plane in R.
R1+kR2=R3
Using knowledge of 1 point on a plane + normal vector (n) to the plane
Since we used vectors and dot product, this applies in Rn
Augmented Matrices
General Case: n equations, n unknowns
1) a1x1+a2x2.+anxn=b
2) a1x1+a2x2.+anxn=b
3) a1x1+a2x2.+anxn=b
.
.
.
4) anxn+anxn.+anxn=b
solve such systems to reduce them to nice forms by elementary row operations:
row echelon form
leading nonze
Ch. 1
A linear equation in a single variable x has form: ax=b
If not, i ts a nonlinear equation in 1 variable.
Ex: ax2+bx +c=0 less than or equal to 2 solutions
sin(x)=0 infini te number of
solutions
ax5+bx4+cx3+dx 2+ex+f=0 5 or less solutions, no quadrat
Look at sloluctions of linear systems: 3.4
and 3.5 (less important)
AxB= RC
Main results for linear systems:
Ax0=b
Suppose x0 is a particular solution of (*)
Ax0=b (1)
Suppose x is any solution of (*)
Ax=b (2)
Find using a and 2 a mtrix vector equation wi
Applied Math 1411b (Linear Algebra for Engineers) Assignment 4
Not to be handed in. Remember that if you are having diculty you should try more
problems than those just indicated below (especially in 1.3 and 1.4 depending on your background). Section 4.1
Applied Math 1411b (Linear Algebra for Engineers) Assignment 3
* Problems are due in the appropriate box in MC 255 by 3:33 pm on January 28. Note
that section 3.5 is covered lightly.
Reminder to make sure you have the Sharp EL510RB the only calculator pe
Applied Math 1411b (Linear Algebra for Engineers) Assignment 2
Not to be handed in. Remember that if you are having diculty you should try more
problems than those just indicated below. Note that Quiz 1 in the week of Jan 17  24 will
test material on Ass
Applied Math 1411b (Linear Algebra for Engineers) Assignment 1
* Problems are due in the appropriate box MC 255 by 3:33 pm on January 17.
On the front page of your assignment you should give your name, student ID number,
tutorial time and day. Finally you
./ ~__i.
Scrum/w Fm "rem AM 10/13 Peer/won.
,
l. (3) Give the augmented matrix corresponding to the system: '
3m+3y+7z = 13 a 3 7 (3 l
2: + y + 2z 2 4 Augmented matrix 2 i I 2 4, / /]
:11? + 42} 7178:: : 16 4. 2,1. g [6 I
(1)) Reduce the matrik A to
~ # 1 ~ # 211 # 3 ~Total ~
~ 12 1118
II 20 ~ 50 ~
~ h S IIJ:o~lfl
I~
~
4Lr;,
Use the determinant test or any method of your to determine
following vectors in parts a) and b) form a basis for iR3
la)
S,
= cfw_[
~6 ].[
n[3
3
wheat her the
]
R\\'R~
~
~G
)~
~Part A
~ 20
~\G
~Part B
~Total
~ 30
~ 50
113D
~llG
~
~
~ ~ c/o
II
Part A (20 marks). :NIarkthe correct answer.
ax + by + cz
2
v
ril
x+bcy =:i  \

\~
+ (a + b)xy
= xzc
1t
ex
=0
(a) is linear iPcfw_~y~z
and linear in cfw_a,b ;
(b) is linearincfw_x,y,z
Assignment, Test and Quiz Schedule for AM 1411 2011
For * Assignments (denoted A 1* etc) you should hand in the * problems
in those assignments by 3:33 pm of the designated day in MC 255 in the
appropriate box.
Doing a quiz in any other than your designat
Chapter 3
3.1:
R2,R3,Rn
Above are examples of vector spaces (ch. 4)
Illustrate the vector properties below using arrow representation of vectors
Not only you will need geometric pictures but also algebraic demonstration
EX:
Show u, v in Rn that u+v is als
l es t hen set rif last nonzer ovar iables t o par amet er s or solve by back subst it ut ion
Consist ent emaining fr ee r ow in not k=0
Leading variables of a ref correspond to the leading nonzero entries in each row of the ref
Remaining variables are c
The University of Western Ontario Applied Mathematics 025 Sample Tutorial Test for week of 12 November 2006 Time: 60 minutes
Use the scantron sheet to answer questions in part A. Use this examination book to answer questions in part B. Part A is worth 50%