Augmented Matrices  page 1
Using Augmented Matrices to Solve Systems of Linear Equations
1.
Elementary Row Operations
To solve the linear system
algebraically, these steps could
be used.
x
5
y
z
11
3
z
12
2
x
4
y
2
z8
+ 
=
=
+=
All of the following operations yield a system which is
equivalent
to the original.
(Equivalent
systems have the same solution
.)
Interchange equations 2 and 3
x
5
y
z
11
2
x
4
y
2
3
z
12
=
Multiply equation 3 by
1
3
x
5
y
z
11
2
x
4
y
2
z1
=
Multiply equation 2 by
1
2

x
5
y
z
11
x
2
y
z4

 +
=
Add equation 1 to 2 and replace
x
5
y
z
11
3
y
15
=
equation 2 with the result
1
3
x
5
y
z
11
y5
=
and add it
5

xz
14
=
=
to equation 1; replace equation 1 with
the result
Add equation 3 to equation 1; replace
x
18
=
=
equation 1 with the result
The solution is (18
,
5
, 4).
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 Spring '10
 Wang
 Calculus, Linear Algebra, Linear Equations, Equations, Matrices, Systems Of Linear Equations, Row, elementary row operations

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