[
Len3+k01[l: :4)? m:
l
o
2. Let l/V be the two dimensional subspace of R4 dened by the equations
(El-T1310
$233H1E420
(a) Find a basis for W'. Hint: TV is the null space of a 2 x 4 matrix aSSOCiated to the equations
above. [K 7C _3 l O]
_ 1" 3 _ A
mi Mtw

Name: SO! UlLiol/l 3
Math 2700 QUIZ Tuesday, March 31
Calculators may only be used to for ordinary arithmetic;
Calculators may not be used for matrix operations.
Time Limit: 20 minutes
1. Calculate the following determinant. You must Show all work. You ma

Name: go [ Ulcfw_On 3
Math 2700 QUIZ - Tuesday, February 17
No Calculators.
Time Limit: 15 minutes
1. Let
1 5 4
A: 2 12 3 l
5 l3 1
Do the columns of A span R3? Explain how you know and Show all your work.
.vo+.
1 ~13 4! '5 "L/
S [a i 5 3 d
R'sSRHM 1 ms

Name: m
Math 2700 QUIZ ~ Thesday, April 21
Calculators may only be used to for ordinary arithmetic.
Calculators may not be used for matrix operations.
Time Limit: 20 minutes
1. (15 points)
(a) Find the eigenvalues for the matrix [ :3 g ]
~2-x 2
/ mm 3~1/:

2. Each of the following determinants can be seen to be zero without doing any calculation. Explain
Why in each case.
(a) 2 0. Why?
03,0
0
2
2
H030
A ron) 0: OJ/ er0$
= 0. Why?
wal
town:
HOOD-7
Row f :2 Row :2.

Name: M
Math 2700 QUIZ - Tuesday, February 3
Time Limit: 15 minutes
1. Consider the following system of equations:
m1+2w2-$3 : 5
2w1'+ x2 + 4:03 = 1
$1+$2+$3 : 2.
(a) Write the augmented matrix for the above system: (5 points)
' f 3k W I 5
it?!
Lll9v
(0)

Name: go [0me 5
Math 2700 QUIZ , Tuesday, March 10
Calculators may only be used to for ordinary arithmetic;
Calculators may not be used for matrix operations.
Time Limit: 20 minutes
1. Indicate which of the following matrices are invertible. Note that you

1 0 3 _7
v1 = 0 ,' V2 2 , v3 = 2 , and u: *lO
1 g _1 9
Write u as a linear combination of v1, vz, and V3. Show all your Work and demonstrate that
you solved this problem by methods of iinear algebra and not by systematic guessing.
W9. WWW git/Mi 41501104

olu Hons
Name:
Math 2760 QUIZ * Tuesday, May 5
Calculators may only be used to for ordinary arithmetic.
Calculators may not be used for matrix operations.
Time Limit: 25 minutes
1, Let
(a) Find an.
IIVII=4/3rvwz" = q/faq 7/3
(1) Find IEWH.
H w [I 2 412

(c) Use the eigenvalues and eigenvectors you found in parts (a) and (b) on the front to describe
What the linear transformation
m1 W2m1 + 2562
T =
$2 21m + 3172
does to R?
T reies lat! allude, F 2 M +42 Ell/300W [9i]
<1ch MW? M A Obi/MW [ l]
2. (5 point

Math 2700 QUIZ Tuesday, September 15
Time Limit: 25 minutes
1. Solve the matrix equation
[1 i ]x=[:1i]-
Show all work and write your nal answer in parametric vector form. (6 points)
113-5
yl=1+7g
LI 5 C. H 714273
X3-= X3
| 1. 3'! 3. Let
1 D 3 -7
V] = 0 ,

Online integral calculators
Testing your integration skills is not the purpose of this course. For indefinite integrals, you are free to
consult a table of integrals, use a graphing calculator or any online integral calculator such as the ones
listed belo

Math 3410, material for final exam
1.1: Basic mathematical models, direction fields
1.2: Solutions of some differential equations
1.3: Classification of differential equations
2.1: Linear equations; method of integrating factors
2.2: Separable equati

Math 3410 - Review for Exam 2
(March 2015)
P. Allaart
SHOW ALL YOUR WORK! NO WORK=NO CREDIT!
1. Check that the differential equation
y 2 3x2 + (2xy + y 2 )y 0 = 0
is exact, and solve the equation.
2. Solve the initial value problem
y 00 4y 0 21y = 0,
y(0)

MATH 2700 - Final Exam Review
Here are some sample problems to review for the final. This is not an exhaustive list; you should study the previous review sheets and exams
as well. I have included answers. I may or may not have time to write up full
soluti

MATH 2700 - Exam 1 - Sample Problems
1. True or False: If a system of linear equations has two different solutions, then
it must have infinitely many solutions. Explain your answer.
2. Solve the following system of equations:
x1
x2
+
2x3
=
3
3x1
4x2
+
5x

MATH 2700 - Practice Problems - Exam 3
1. Let M33 be the vector space of 3 3 matrices. What is the dimension
of M33 ? Now let H be the subset of matrices A so that det(A) = 0. Decide
whether or not H is a subspace.
x1
2. Verify that the set, V , of column

MATH 2700 - Review Problems - Exam 2
1. Let A =
2
3
4
1
3
5
!
, and B =
1
2
3
5
1
3
!
. Calculate 3A 2B.
2. Multiply in whichever orders are possible (AB or BA or both).
!
2 2
1 3
.
A= 4
5 , B =
2 1
3 4
3. For two n n matrices A and B the Lie
by
! bracket