Ben Cooke
Math 107
Test 2
•
Do not open this test booklet until you are directed to do so.
•
You have 50 minutes to earn 100 points.
•
This exam is closed book. You are not allowed to use a calculator.
•
Show your work, as partial credit will be given.
•
Do not spend too much time on any one problem. Read them all through first and attack
them in the order that allows you to make the most progress.
•
Sign the affirmation of the Duke community standard after you complete the test and before
you turn it in.
Problem
Points
Grade
Name
−
1
40
2
25
3
35
Total
100
Name:
1
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Ben Cooke
Math 107
1.
(40 points)
Given the matrix A,
A
=
1
2
3
4
2
3
−
1
−
2
−
3
−
4
5
8
(a) Find a basis for the nullspace of
A
.
(b) Find a basis for the row space of
A
and determine if
1
2
−
1
−
2
is in the row space.
(c) What is the rank of
A
? the dimension of the nullspace of
A
?
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 Spring '07
 Trangenstein
 Math, Linear Algebra, Duke Community Standard, Ben Cooke

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