MATH340, Fall 2015 EXAM II Colorado State University
5:00-7:00PM, Oct 12, 2015
Section: Name:
• You have two hours to complete this exam.
• No notes, books, or other references are allowed during this exam.
• Calculators are not allowed during the exam.
• A two-sided cheat sheet of 8
2
1
00
× 11
00 or smaller is allowed during the exam.
• There are questions on the front of the page. You can use the back of each page if you need more space. If you do use any extra paper, make sure that your name is on it and that you attach it to your exam.
• You must show all work to receive credit. Answers for which no work is shown will receive no credit unless specifically stated otherwise.
Question Score Maximum
1 12
2
3
18
15
4
5
6
20
20
15
Total 100
1

MATH340, Fall 2015 EXAM II Colorado State University
1.
( 12 points ) True (T) or False (F) problems (circle T or F only, no partial credit):
(i) T or F A 2 × 2 matrix may have a real eigenvalue and an imaginary eigenvalue.
(ii) T or F Second order equation x
00
+ µ ( x 2 − 1) x
0
+ can not be written as a system of first-order equations.
x = 0 is nonlinear, and therefore
(iii) T or F Although by definition e
A
=
∞
X
A k
, but for some matrices we can have exact k !
expansions for some finite N such that k =0 e
A
=
N
X
A k !
k
.
k =0
(iv) T or F A k = 0 for some finite k if and only if A is singular.
(v) T or F The general solution for 4 x
00
+ 4 x
0
+ 17 x = 0 is x ( t ) = e
− t/ 2 ( c
1 cos(2 t ) + c
2 sin(2 t )) for some constants c
1
, c
2
.
(vi) T or F The function x ( t ) = e t
+ e
− 2 t
3 x
00
− 4 x = 0.
is a solution to the third-order equation x
000
+
2