1
Appendix SA
Solution of Linear Simultaneous Equations
SA.1
System of Linear Simultaneous Equations
A system of
n
linear simultaneous equations may be written in the standard form
as follows:
a
11
x
1
+
a
12
x
2
+
a
13
x
3
+
•
•
•
+
a
1
n
x
n
=
B
1
a
21
x
1
+
a
22
x
2
+
a
23
x
3
+
•
•
•
+
a
2
n
x
n
=
B
2
a
31
x
1
+
a
32
x
2
+
a
33
x
3
+
•
•
•
+
a
3
n
x
n
=
B
3
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
a
n1
x
1
+
a
n2
x
2
+
a
n3
x
3
+
•
•
•
+
a
nn
x
n
=
B
n
(SA.1.1)
where
x
1
, x
2
,
…
, x
n
are the unknowns, or dependent variables, whose values are to be
determined in terms of the
B
’s and the
a
ij
coefficients. These coefficients, which in
general could be complex numbers, may be ordered in an
n
×
n
array as follows:
nn
n
n
n
n
n
a
a
a
a
a
a
a
a
a
a
a
a
3
2
1
2
23
22
21
1
13
12
11
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
=
Δ
(SA.1.2)
where the
i
and
j
subscripts in a
ij
denote, respectively, the
i
th row and
j
th column in the
array.
The array (SA.1.2) is known as the
determinant
of the set of simultaneous
equations and is denoted by the symbol
Δ
. The determinant is a number whose value is
evaluated according to certain rules.

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