Solutions of simultaneous equations – HP 33s User Manual
Page 234
15–12
Mathematics Programs
125
g
@
)
Sets T equal to 125.
63
g
@
)
Sets P equal to 63.
X
D
/
)
Calculates dot product.
g
/
)
Calculates angle between
resultant force vector and lever.
g
@
)
Gets back to input routine.
Solutions of Simultaneous Equations
This program solves simultaneous linear equations in two or three unknowns. It
does this through matrix inversion and matrix multiplication.
A system of three linear equations
AX
+ DY + GZ = J
BX
+ EY + HZ = K
CX
+ FY + IZ = L
can be represented by the matrix equation below.
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L
K
J
Z
Y
X
I
F
C
H
E
B
G
D
A
The matrix equation may be solved for X, Y, and Z by multiplying the result matrix
by the inverse of the coefficient matrix.
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Z
Y
X
L
K
J
I
F
C
H
E
B
G
D
A
Specifics regarding the inversion process are given in the comments for the
inversion routine, I.