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Solutions of Simultaneous Equations—
Matrix Inversion Method
This program solves simultaneous linearequations 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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