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MATH 17100
28446
11/04/2009
Systems of Linear Equations and Elementary Row operations
Given the system of
m
linear equations
in
n
unknowns
12
,,,
n
xx
x
:
11 1
12 2
1
1
nn
ax ax
ax b
+
++
=
………….
.
(1)
21 1
22 2
2
2
11
2 2
(2)
()
m
m
mn n
m
m
+
=
+
=
..................
..................
we can
recast
them in
matrix form
:
=
Ax
b
.
Here
A
is the
mn
×
coefficient matrix
11
12
1
21
22
2
n
n
m
m
mn
aa
a
a
a
,
x
is the
1
n
×
matrix
1
2
n
x
x
x
, the components being the unknowns of the system of equations to be
solved for,
b
is the
1
m
×
matrix
1
2
m
b
b
b
.
The
augmented matrix
[
A

b]
is the
(
1)
×+
matrix that has the column matrix
b
appended
to the right of A :
[A

b]
=
11
12
1
1
21
22
2
2
n
n
m
m
mn
m
a a
ab
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View Full Document Each row in the augmented matrix corresponds to an equation in the given system of equations.
The usual procedure followed in the solution procedure called the
Method of Elimination
consists of the three types of operations:
(1)
Interchange
of two
equations
(2)
Multiply
ing an
equation
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This note was uploaded on 11/04/2010 for the course MATH 17100 taught by Professor Kitchens during the Spring '10 term at IUPUI.
 Spring '10
 KITCHENS
 Linear Equations, Equations, Systems Of Linear Equations

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