Civil Engineering Reference
In-Depth Information
Also, the final row of the new matrix is found by:
a
a
1
<≤
≠
jm
1
j
b
=
where
nj
, −
1
a
0
11
11
where,
a
elements in old matrix A
b
elements in new matrix B
i
row number in old matrix A (
n
)
j
column number of old matrix A (
m
)
For example,
=− =−
−
()
=
ba
aa
a
22
2
12 21
,
,
3
5
22
,
22
,
11
From these equations, column 1 is reduced.
517
−
9
2
19
2
[]
=
2
−−
5
2
13
2
−
1
Following the process again to reduce column 2:
41
10
123
10
−−
23
10
79
10
[]
=
1
5
7
5
−
Finally, one more cycle reduces column 3 and obtains the solution:
1
2
3
[]
=
It is known that applying these equations to a number of simultaneous
equations,
n
, will produce the same number of matrices,
n
, to achieve the
solution.
