Math 2902 section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 1: due Wednesday, January 11
1. Use the abstract properties of the dot product to show that, for all subspaces W of Rn , the
orthogonal complement W is also a s
Math 2902 sections 43 and 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 2: due Friday, January 20
Suppose three species live in symbiosis in a certain ecosystem: a plant, a fungus, and an insect.
The plants depend on the fun
Math 2902 sections 43 and 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 6: due Friday, February 24
On the last assignment, you studied homogeneous linear systems of ordinary differential equations
of the form
dy
= Ay,
dt
whe
Math 2902 Section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus
Quiz 5: Tuesday, February 14
KEY
1. State whether each of the following statements are TRUE or FALSE, and briey justify your
answers.
(a) (3pts.) lim 3: + y = 0.
(mam) $2 +
Math 2902 Section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus
Quiz 6: Tuesday, February 21
Name: Eigl
1. State whether each of the following statements are TRUE or FALSE, and briey justify your
answers.
(a) (3pts.) If you begin at the
0/
all
Math 2902 Section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Quiz 4: Tuesday, February 7
Name: [llC: i _._
1. (513135.) Use the fact that tan(t) : Si"( to compute %(tan(t). Dont just write down the
cos(t
answer, if you hap
Math 2902 Section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Quiz 1: Tuesday, January 10
Name: E
1. Are the following statements TRUE or FALSE? Justify your answer. Each is worth 2 points.
)Every orthogonal set of vectors is linear
  N : K .
North western UH] VEI'SI tySt:nE%
Math 2902 Midterm 1
Winter Quarter 2012
Tuesday, January 31, 2012
(2 points) Put a check mark next to your section:
lI'I_I
IiII
Instructions:
0 Read each problem carefully.
o Write legibly.
: Show all y
Northwestern UniversityName AL
Student ID:
Math 2902 Midterm 2
Winter Quarter 2012
Monday, February 27, 2012
(1 point) Put a check mark next to your section:
Cyr Gutzwiller 10am j
Cutrone Gutzwiller 12pm J
Instructions:
Question Possible Score 0 Read e
Math 2902 Section 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Quiz 2: Tuesday, January 17
Name: E
1. Are the following statements ALWAYS true, only SOMETIMES true, or NEVER true?
Justify your answers. Each is worth 2 points.
(a) If
Math 2902 sections 43 and 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 3: due Friday, February 10
1. Suppose that y(t) represents an interesting population at time t; the simple exponential
growth model, y 0 = ky, is often
Math 2902 sections 43 and 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 3: due Friday, January 27
1. Changing variables in a quadratic form is almost never worth your time and energy, and this
problem will show you how to av
Math 2902 sections 43 and 61, Winter 2012
MENU: Linear Algebra and Multivariable Calculus II
Homework 5: due Friday, February 17
Often we are interested in studying several related quantities that are all changing over time.
For example, suppose that we
Math 2902: Proof of Theorem from Class
Wednesday, January 11
Theorem: If A is an n m matrix, then
1. (im A) = ker(AT ),
2. ker(A) = ker(AT A), and
3. ker(A) = cfw_~0 if and only if AT A is invertible.
 

Proof. Let V = im(A) where A = ~v1 ~v2 ~vm for