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Page 11-28
The procedure for the case of “dividing” b by A is illustrated below for the case
2x
1
+ 3x
2
–5x
3
= 13,
x
1
– 3x
2
+ 8x
3
= -13,
2x
1
– 2x
2
+ 4x
3
= -6,
The procedure is shown in the following screen shots:
The same solution as found above with the inverse matrix.
Solving multiple set of equations with the same coefficient matrix
Suppose that you want to solve the following three sets of equations:
X +2Y+3Z = 14, 2X +4Y+6Z = 9, 2X +4Y+6Z = -2,
3X -2Y+ Z = 2, 3X -2Y+ Z = -5, 3X -2Y+ Z = 2,
4X +2Y -Z = 5, 4X +2Y -Z = 19, 4X +2Y -Z = 12.
We can write the three systems of equations as a single matrix equation: A⋅X
= B, where
The sub-indices in the variable names X, Y, and Z, determine to which equation
system they refer to. To solve this expanded system we use the following
procedure, in RPN mode,
,,
124
123
321
)3()2()1(
)3()2()1(
)3()2()1(
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−=
ZZZ
YYY
XXX
XA
.
12195
252
2914
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
=B