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previous section. 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
,
,
1
2
4
1
2
3
3
2
1
)
3
(
)
2
(
)
1
(
)
3
(
)
2
(
)
1
(
)
3
(
)
2
(
)
1
(
=
−
−
=
Z
Z
Z
Y
Y
Y
X
X
X
X
A
.
12
19
5
2
5
2
2
9
14
−
−
=
B
