Civil Engineering Reference
In-Depth Information
Equation 2.5a is divided by the first unknown in that equation, −41/10
and the new Equation 2.6a is multiplied by the corresponding coefficient
of that unknown from the two other equations (2.5b and 2.5c) to yield
Equations 2.6b and 2.6c.
x
3
=
3
(2.6a)
23
10
69
10
x
=
(2.6b)
1
5
3
5
− −
x
(2.6c)
Equation 2.6b is subtracted from 2.5b and becomes 2.7a. Equation 2.6c is
subtracted from 2.5c and becomes 2.7b. Equation 2.6a now becomes 2.7c.
All the unknowns are found with the following solution:
x
1
=
1
(2.7a)
x
2
=
2
(2.7b)
x
3
=
3
(2.7c)
The same result may be obtained by working with just the coefficients
and constants of the equations. Given the same equations, the following
augmented matrix is valid:
225 3
xxx
−+=
1
2
3
234 0
xxx
++=
1
2
3
3
xx x
−+ =
3
10
1
2
3
22513
23420
3
−
[]
=
A
−11310
An augmented matrix, [
B
], is established from the following algorithm:
1
1
<≤
<≤
≠
in
jm
aa
a
ji
−−
=−
11
b
a
where
i
11
,
j
ij
11
a
0
11
