|
|
|
serve file 25.pdf
serve_file_25.pdf
Showing 3-8 out of 12
MA | 262 | Linear Algebra and Differential Equatio...
MA | 262 | Linear Algebra and Differential Equations | exam |MA262 — FINAL EXAM — SPRING 2016 — MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and use a # 2 pencil to fill in the required information on the scantron. 3. MARK YOUR TEST NUMBER ON YOUR SCANTRON 4. Once you are allowed to open the exam, make sure you h
MA | 262 | Linear Algebra and Diffe...
MA | 262 | Linear Algebra and Differential Equations | exam |MA262 — FINAL EXAM — SPRING 2016 — MAY 2, 2016 TEST NUMBER 01 INSTRUCTIONS: 1. Do not open the exam booklet until you are instructed to do so. 2. Before you open the booklet fill in the information below and use a # 2 pencil to fill in the required information on the scantron. 3. MARK YOUR TEST NUMBER ON YOUR SCANTRON 4. Once you are allowed to open the exam, make sure you h
Page 3
3.
Let
y
(
x
) be the solution to the initial value problem
dy
dx
=
y
x
(ln
x
)
2
and
y
(
e
)=
e.
Then ln
y
(
e
2
) is equal to
A. 2
B. 3
C.
3
4
D.
3
2
E. 1
4.
Let
y
(
x
) satisfy the following initial value problem
(3
x
2
e
xy
+
x
3
ye
xy
)
dx
+(
x
4
e
xy
)
dy
=0
,
y
(1) = 0
.
Then
y
(2) is equal to
A. ln 2
B.
-
ln 2
C.
3
4
ln 2
D.
-
2
3
ln 2
E.
-
3
2
ln 2
Page 4
5.
Let
y
(
x
) satisfy the following initial value problem
y
′′
+
y
-
1
(
y
′
)
2
=
y
-
1
e
-
y
y
′
,
y
(0) = 1
,y
′
(0) = 1
.
Then
V
(
x
)=
y
′
(
x
) satisfies
A.
V
(
x
)=
y
-
1
(1 +
1
e
-
e
-
y
)
B.
V
(
x
)=
1
2
y
-
1
(2 +
1
e
-
e
-
y
)
C.
V
(
x
)=
-
y
-
1
e
-
y
+
1
e
+1
D.
V
(
x
)=
y
-
1
(1
-
1
e
+
e
-
y
)
E.
V
(
x
)=
3
2
y
-
1
(
2
3
-
1
e
+
e
-
y
)
6.
The rank of
1
2
1
4
0
1
3
1
3
7
6
13
2
5
5
9
is equal to
A. 3
B. 4
C. 1
D. 0
E. 2
Page 5
7.
Let
T
:
R
3
-→
R
5
be the Linear transformation given by
T
(
x
)=
Ax,
where
A
=
1
2
3
2
1
4
1
-
1
1
0
-
3
-
2
1
1
1
.
Then the dimension of the range of
T
is equal to
A. 1
B. 2
C. 3
D. 4
E. 5
8.
Let
A
=
-
1
0
0
1
5
-
1
1
6
-
2
. Let
λ
1
,λ
2
and
λ
3
denote the eigenvalues of
A
and let
E
1
,E
2
and
E
3
denote the corresponding eigenspaces. Which of the following is correct?
A.
λ
1
=2
,λ
2
= 3 and
λ
3
=
-
1
,
dim
E
1
= dim
E
2
= dim
E
3
=1
B.
λ
1
=
λ
2
=
-
1
,λ
3
=4
,
dim
E
1
= dim
E
2
=2
,
dim
E
3
=1
C.
λ
1
=
λ
2
=
-
1
,λ
3
=4
,
dim
E
1
= dim
E
2
=1
,
dim
E
3
=1
D.
λ
1
=1
,λ
2
=
λ
3
=4
,
dim
E
1
=1
,
dim
E
2
= dim
E
3
=2
E.
λ
1
=
λ
2
=
-
1
,λ
3
=3
,
dim
E
1
= dim
E
2
=2
,
dim
E
3
=1
Page 6
9.
Find all values of
α
such that the vectors (1
,
0
, α/
4
,
1)
,
(2
,
0
,
1
,α
) and (1
,
0
,
1
,
2) are linearly
dependent
A.
α
= 1 and
α
=2
B.
α
= 2 and
α
=6
C.
α
= 2 and
α
=4
D.
α
=
-
2 and
α
=4
E.
α
= 3 and
α
=6
10.
Let
A
and
B
be square matrices such that det(
A
) = 5 and det(
A
+
B
) = 20
.
We conclude that
det(
I
+
A
-
1
B
) is equal to
A. 4
B. 3
C. 5
D. 10
E. 8
Page 7
11.
Let
M
3
(
R
) be the space of 3
×
3 matrices with real entries and let
S
be the subspace of
M
3
(
R
)
such that the sums of the elements of each row is equal to zero. The dimension of
S
is equal to
A. 3
B. 4
C. 1
D. 2
E. 6
12.
A particular solution to the equation
(
D
2
-
2
D
+ 10)
2
y
=
e
x
sin 3
x
+ cos 2
x,
(which does not contain terms that solve the homogeneous equation) has the form
A.
y
p
(
x
)=
e
x
(
A
1
cos 3
x
+
B
1
sin 3
x
+
A
2
x
cos 3
x
+
B
2
x
sin 3
x
+
A
3
x
2
cos 3
x
+
B
3
x
2
sin 3
x
)+
A
5
cos 2
x
+
B
5
sin 2
x
B.
y
p
(
x
)=
e
x
(
A
1
x
cos 3
x
+
B
1
x
sin 3
x
+
A
2
x
2
cos 3
x
+
B
2
x
2
sin 3
x
)+
A
3
cos 2
x
+
B
3
sin 2
x
C.
y
p
(
x
)=
e
x
(
A
1
cos 3
x
+
B
1
sin 3
x
)+
A
2
cos 2
x
+
B
2
sin 2
x
D.
y
p
(
x
)=
e
x
(
A
1
x
2
cos 3
x
+
B
1
x
2
sin 3
x
)+
A
2
cos 2
x
+
B
2
sin 2
x
E.
y
p
(
x
)=
e
x
(
A
1
x
cos 3
x
+
B
1
x
sin 3
x
)+
A
2
cos 2
x
+
B
2
sin 2
x
Page 8
13.
Find the general solution to the differential equation
y
(4)
-
8
y
′′
+ 16
y
=0
.
A.
y
=
c
1
e
2
x
+
c
2
e
-
2
x
B.
y
=
c
1
xe
2
x
+
c
2
xe
-
2
x
C.
y
=
c
1
e
2
x
+
c
2
e
-
2
x
+
c
3
xe
2
x
+
c
4
xe
-
2
x
D.
y
=
c
1
xe
2
x
+
c
2
xe
-
2
x
+
c
3
x
2
e
2
x
+
c
4
x
2
e
-
2
x
E.
y
=
c
1
cos 2
x
+
c
2
sin 2
x
+
c
3
x
cos 2
x
+
c
4
x
sin 2
x
14.
Which of the following is a Green’s function of the differential equation
y
′′
-
3
y
′
+2
y
=
F
(
x
)?
(
K
(
x, t
)=
1
W
[
y
1
,y
2
](
t
)
(
y
1
(
t
)
y
2
(
x
)
-
y
2
(
t
)
y
1
(
x
)))
A.
K
(
x, t
)=(
e
2
x
+4
t
-
e
x
+5
t
)
B.
K
(
x, t
)=(
e
2(
x
-
t
)
-
e
(
x
-
t
)
)
C.
K
(
x, t
)=(
e
3(
x
+
t
)
-
e
x
+
t
)
D.
K
(
x, t
)=(
e
4(
x
-
t
)
-
e
5(
x
-
t
)
)
E.
K
(
x, t
)=(
e
3(
x
-
t
)
+
e
2(
x
-
t
)
)
Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
Purdue University-Main Ca...
Purdue_University-Main_Campus
School:
Linear_Algebra_and_Differential_Equations
Course:
Great resource for chem class. Had all the past labs and assignments
Leland P.
Santa Clara University
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades
Know more
Students also viewed documents
lab 18.docx
lab_18.docx
Course
Course
3
Module5QuizSTA2023.d...
Module5QuizSTA2023.docx.docx
Course
Course
10
Week 7 Test Math302....
Week_7_Test_Math302.docx.docx
Course
Course
30
Chapter 1 Assigment ...
Chapter_1_Assigment_Questions.docx.docx
Course
Course
5
Week 4 tests.docx.do...
Week_4_tests.docx.docx
Course
Course
23
Week 6 tests.docx.do...
Week_6_tests.docx.docx
Course
Course
106
