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Math 20D.
Midterm Exam 2
May 22, 2009
Turn off and put away your cell phone.
No calculators or any other electronic devices are allowed during this exam.
You may use one page of notes, but no books or other assistance during this exam.
Read each question carefully, and answer each question completely.
Show all of your work; no credit will be given for unsupported answers.
Write your solutions clearly and legibly; no credit will be given for illegible solutions.
If any question is not clear, ask for clarification.
#
Points
Score
1
8
2
8
3
10
Σ
26
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1. (8 points) Consider the system of two first order initial value problems
braceleftbigg
x
′
1
= 2
x
1
+ 4
x
2
, x
1
(0) = 4
x
′
2
=
x
1

x
2
,
x
2
(0) = 1
(a) Write the system of initial value problems as a matrix initial value problem
x
′
=
Ax
,
x
(0) =
parenleftbigg
x
1
(0)
x
2
(0)
parenrightbigg
.
(b) Solve the matrix initial value problem. Be sure your solution
x
(
t
)
satisfies the
initial condition
x
(0) =
parenleftbigg
x
1
(0)
x
2
(0)
parenrightbigg
.
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 Spring '09
 Eggers,John
 Eigenvalue, eigenvector and eigenspace, The Matrix Reloaded, matrix initial value

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