HP 50G, Руководство пользователя

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Page 11-18
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Using the numerical solver for linear systems
There are many ways to solve a system of linear equations with the calculator.
One possibility is through the numerical solver
‚Ï
. From the numerical
solver screen, shown below (left), select the option 4. Solve lin sys.., and press
@@@OK@@@
. The following input form will be provided (right):
To solve the linear system A
⋅
x = b , enter the matrix A , in the format [[ a
11
, a
12,
… ], … [….]] in the A: field. Also, enter the vector b in the B: field. When the
X: field is highlighted, press [SOLVE]. If a solution is available, the solution
vector
x will be shown in the X: field. The solution is also copied to stack level
1. Some examples follow.
A square system
The system of linear equations
2x
1
+ 3x
2
–5x
3
= 13,
x
1
– 3x
2
+ 8x
3
= -13,
2x
1
– 2x
2
+ 4x
3
= -6,
can be written as the matrix equation A
⋅
x = b , if
m n
nm n n
m
m
a a a
a a a
a a a
A
×
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
L
M O M M
L
L
2 1
2 22 21
1 12 11
1
2
1
×
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
m
m
x
x
x
x
M
1
2
1
×
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
n
n
b
b
b
b
M
.
6
13
13
, ,
4 2 2
8 3 1
5 3 2
3
2
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
− =
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−
−
= b x A
and
x
x
x