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October 9, 2014 q I, . ' s ' g 7
MTH215-0002 Exam 1 - " ' " '
Please Show all work, including row operations, and indicate your nal answer to
each question clearly. Many questions have multiple parts, so make sure youve
answered them all before
MTH 307 Barrus
Homework 2
Fall 2014
These notes are copyrighted by Michael D. Barrus. Any duplication or transmission
in either hard copy or digital form without prior written consent is strictly prohibited.
This includes, but is not limited to, posting a
Name:
October 9, 2014
MTH2150002 Exam 1
Please Show all work, including row operations, and indicate your nal answer to
each question clearly. Many questions have multiple parts, so make sure youve
answered them all before moving onto the next problem.
1.7 Linear Independence
A homogeneous system such as
12
3
x1
35
9
x2
59
3
0
x3
0
0
can be viewed as a vector equation
1
x1
3
5
2
x2
5
9
3
x3
9
0
3
0
.
0
The vector equation has the trivial solution (x 1 0, x 2 0,
x 3 0), but is this the only solution?
D
1.5 Solutions Sets of Linear Systems
Homogeneous System:
Ax 0
(A is m
n and 0 is the zero vector in R m
EXAMPLE:
x1
10x 2 0
2x 1 20x 2 0
Corresponding matrix equation Ax 0:
1 10
x1
2 20
x2
0
0
Trivial solution:
x
0
0
or
x0
The homogeneous system Ax 0 alw
MTH 307 Barrus
Homework 8
Fall 2014
These notes are copyrighted by Michael D. Barrus. Any duplication or transmission
in either hard copy or digital form without prior written consent is strictly prohibited.
This includes, but is not limited to, posting a
MTH 307 Barrus
Homework 7
Fall 2014
These notes are copyrighted by Michael D. Barrus. Any duplication or transmission
in either hard copy or digital form without prior written consent is strictly prohibited.
This includes, but is not limited to, posting a
MTH 307 Barrus
Homework 6
Fall 2014
These notes are copyrighted by Michael D. Barrus. Any duplication or transmission
in either hard copy or digital form without prior written consent is strictly prohibited.
This includes, but is not limited to, posting a
MTH 307 Barrus
Homework 3
Fall 2014
These notes are copyrighted by Michael D. Barrus. Any duplication or transmission
in either hard copy or digital form without prior written consent is strictly prohibited.
This includes, but is not limited to, posting a
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1.6 Linear Independence
Recall, for example, that the solution sets of
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The vector equation has the trivial solution (x 1
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MTH 215
Quiz 3 (20 points)
Sections 4.1 4.6
DUE NOV. 1, 2011 AT 9:30 AM. NO LATE QUIZZES WILL BE ACCEPTED.
You MUST show ALL of your work on every problem to receive credit.
If you use a definition or theorem as a step in your solutions, you must cite it.
MTH 215
Quiz 1 Solutions
1.
There is a Fact on p. 43 of your textbook that states The homogeneous equation
Ax = 0 has a non-trivial solution if and only if the equation has at least one free
variable. Prove this Fact.
Let Ax = 0 have a non-trivial solutio
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