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Chapter 8
Linear Algebraic Equations
and Matrices
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View Full Document Three individuals connected by bungee cords
Freebody diagrams
Newton’s
second law
=


=



+
=


+
0
x
x
k
g
m
0
x
x
k
x
x
k
g
m
0
x
k
x
x
k
g
m
2
3
3
3
1
2
2
2
3
3
2
1
1
1
2
2
1
)
(
)
(
)
(
)
(
=
+

=

+

=

+
g
m
x
k
x
k
g
m
x
k
x
k
k
x
k
g
m
x
k
x
k
k
3
3
3
2
3
2
3
3
2
3
2
1
2
1
2
2
1
2
1
)
(
)
(
Rearrange the equations
[
K
] {
x
} = {
b
}
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View Full Document Newton’s second law – equation of motion
Kirchhoff’s current and voltage rules
Massspring
system
(similar to
bungee jumpers)
Resistor
circuits
❚
Solved single equations previously
❚
Now consider more than one variable and more
than one equation
( 29
0
x
f
=
( 29
( 29
( 29
0
x
,...,
x
,
x
f
0
x
,...,
x
,
x
f
0
x
,...,
x
,
x
f
n
2
1
n
n
2
1
2
n
2
1
1
=
=
=
Linear Algebraic Equations
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View Full Document ❚
Linear equations and constant coefficients
❚
a
ij
and
b
i
are constants
n
n
nn
2
2
n
1
1
n
2
n
n
2
2
22
1
21
1
n
n
1
2
12
1
11
b
x
a
...
x
a
x
a
b
x
a
...
x
a
x
a
b
x
a
...
x
a
x
a
=
+
+
+
=
+
+
+
=
+
+
+
Linear Systems
}
{
}
]{
[
]
[
]
][
[
b
x
A
or
b
x
A
=
=
=
n
2
1
n
2
1
nn
2
n
1
n
n
2
22
21
n
1
12
11
b
b
b
x
x
x
a
a
a
a
a
a
a
a
a
Mathematical background
❚
It is convenient to write system of equations
in matrixvector form
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View Full Document[ ]
=
mn
4
m
3
m
2
m
1
m
n
4
44
43
42
41
n
3
34
33
32
31
n
2
24
23
22
21
n
1
14
13
12
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Fall '09 term at University of Florida.
 Fall '09
 RAPHAELHAFTKA

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