Solution Of Linear Systems; Using The Numerical Solver For Linear Systems - HP 50g User Manual
Graphing calculator
Hide thumbs
Also See for HP 50g:
- User manual (887 pages) ,
- Advanced user's reference manual (693 pages) ,
- Quick start manual (47 pages)
Table of Contents
Advertisement
Solution of linear systems
A system of n linear equations in m variables can be written as
a
x
+ a
11
1
12
a
x
+ a
21
1
22
a
x
+ a
31
1
32
.
.
a
x
+ a
n-1,1
1
n-1,2
a
x
+ a
x
n1
1
n2
This system of linear equations can be written as a matrix equation,
= b
A
x
n m
m 1
n 1
a
⎡
11
⎢
a
⎢
21
A
⎢
M
⎢
a
⎣
n
1
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 provide (right):
To solve the linear system A x = b , enter the matrix A , in the format
[[ a
, a
... ], ... [....]] in the A: field. Also, enter the vector b in the B:
11
12,
field.
When the X: field is highlighted, press @SOLVE .
available, the solution vector x will be shown in the X: field. The solution is
also copied to stack level 1. Some examples follow.
The system of linear equations
Page 9-9
x
+ a
x
+ ...+ a
2
13
3
x
+ a
x
+ ...+ a
2
23
3
x
+ a
x
+ ...+ a
2
33
3
.
...
x
+ a
x
2
n-1,3
3
+ a
x
+ ...+ a
2
n3
3
, if we define the following matrix and vectors:
a
L
a
12
1
m
a
L
a
22
2
m
M
O
M
a
L
a
n
2
nm
x
+ a
1,m-1
m-1
x
+ a
2,m-1
m-1
x
+ a
3,m-1
m-1
.
.
+ ...+ a
x
n-1,m-1
x
+ a
n,m-1
m-1
x
⎤
⎡
⎤
1
⎥
⎢
⎥
x
⎥
⎢
⎥
2
x
⎥
⎢
⎥
M
⎥
⎢
⎥
x
⎦
⎣
⎦
m
n
m
m
,
x
= b
,
1,m
m
1
x
= b
,
2,m
m
2
x
= b
,
3,m
m
3
.
+ a
x
= b
m-1
n-1,m
m
x
= b
.
n,m
m
n
b
⎡
⎤
1
⎢
⎥
b
⎢
⎥
2
b
⎢
⎥
M
⎢
⎥
b
⎣
⎦
n
1
n
1
,
If a solution is
,
n-1
Advertisement
Table of Contents
