MATH 415 Final: Math415FinalSpring2018
6 Jan 2021
School
Department
Course
Professor
Math 415 - Final Exam - May 8, 2018
Sections AL1, AL2, AL3, AL4
Full Name: Net ID:
TA Name: TA Section: AD
Instructions
1.There are 40 problems worth
5 points each.
2. You must not communicate
with other students.
3. No books, notes, calculators, or
electronic devices allowed.
4. This is a 3 hour exam.
5. Do not turn this page until
instructed to do so.
6. Bubble in your answers on the scantron
form provided. Also circle your
answers on the exam itself.
7. Hand in both the exam and the scantron.
8. On the scantron make sure you bubble in
your name, your UIN and your NetID.
9. There are several different versions of this
exam so essentially everyone gets their
own unique exam.
Dane: AD3 @ T9 ADB @ R10 ADH @ R1
Elliot: AD2 @ R8 AD4 @ R9
ADC @ T11 ADQ @ T10
Justin: AD7 @T10 ADL @ R3 ADP @R9
ADR @ R10 ADS @ T11
Sam: AD5 @ T3 AD6 @ R3 ADM @ T4
ADN @ R4 ADY @ T2
Derek: AD9 @ T11 ADE @ T12 ADK @ T3
ADT @ R11 ADV @ R12
Daniel: AD8 @ R10 ADA @ T10 ADI @ T2
ADW @ T1 ADZ @ R2
Ruth: ADF @ R12 ADG @ T1 ADJ @ R2
ADU @ T12 ADX @ R1
Fill in the following information on the scantron form:
On the front of the scantron bubble in your name, your UIN and your
NetID! On the back of the scantron bubble in the following:
89. A
90. A
91. A
92. A
93. A
94. D
95. C
96. E
1
Problems from Chapter 1
1. (5 points) Let
S=8
<
:2
4
4
6
63
5,2
4
5
4
33
5,2
4
2
10
123
59
=
;
.
Out of the following vectors:
u=2
4
6
9
93
5,v=2
4
12
11
93
5,w=2
4
2
9
33
5
which are a linear combination of the vectors in S?
(A) Only uand w.
(B) u,v, and w.
(C) Only w.
(D) Only uand v.
(E) Only u.
2
2. (5 points) Consider the following four statements about the linear system Ax = 0:
(I) Ax = 0 may have infinitely many solutions
(II) Ax = 0 may have exactly two solutions
(III) Ax = 0 may have just one solution
(IV) Ax = 0 may have no solution
Which of these possibilities are true?
(A) Only I, III, and IV.
(B) Only I and III.
(C) Only II, III, and IV.
(D) All of the statements are true.
(E) Only I and IV.
3. (5 points) True/False: If A,Bare matrices, and both of the products AB and BA are defined, then
AB and BA are square matrices.
(A) True
(B) False
3
Document Summary
Math 415 - final exam - may 8, 2018. Ad3 @ t9 adb @ r10 adh @ r1. Ad5 @ t3 ad6 @ r3 adm @ t4. Ad9 @ t11 ade @ t12 adk @ t3. Ad8 @ r10 ada @ t10 adi @ t2. Adf @ r12 adg @ t1 adj @ r2. Fill in the following information on the scantron form: On the front of the scantron bubble in your name, your uin and your. On the back of the scantron bubble in the following: a, a, a, a, a, d, c, e. Problems from chapter 1: (5 points) let. S =8< which are a linear combination of the vectors in s? (a) only u and w. (b) u, v, and w. (c) only w. (d) only u and v. (e) only u. Ab and ba are square matrices. (a) true (b) false.
