Solutions
of
Simultaneous
Equations—
Matrix
Inversion
Method
This
program
solves
simultaneous
linear
equations
in
two
or
three
un
knowns. It does this through matrix inversion and matrix
multiplication.
A system of three linear equations
AX + DY + GZ = /
BX + EY +
HZ
= K
CX + FY +
IZ
= L
can be represented by the matrix equation below.
A D G
X
V
B E H Y
=
K
C F I
Z L
The matrix equation may be solved for X,
Y,
and Z by multiplying the
result matrix by the inverse of the coefficient matrix.
A'
U
G'
Y
X
B'
E'
H'
K
=
Y
C
F r L
Z
Specifics regarding the inversion process are given in the comments
for
the
inversion
routine,
I.
12:
Mathematics
Programs
183
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