# Solution Of Linear Systems - HP F2226A - 48GII Graphic Calculator User Manual

Graphing calculator.

The implementation of function LCXM for this case requires you to enter:
2`3`‚@@P1@@ LCXM `
The following figure shows the RPN stack before and after applying function
LCXM:
In ALG mode, this example can be obtained by using:
The program P1 must still have been created and stored in RPN mode.

## Solution of linear systems

A system of n linear equations in m variables can be written as
⋅x
⋅x
a
+ a
11
1
12
2
⋅x
⋅x
a
+ a
21
1
22
2
⋅x
⋅x
a
+ a
31
1
32
2
.
.
.
.
⋅x
⋅x
a
+ a
n-1,1
1
n-1,2
⋅x
⋅x
a
+ a
n1
1
n2
2
This system of linear equations can be written as a matrix equation, A
= b
, if we define the following matrix and vectors:
×
n
1
a
a
11
12
a
a
21
22
A
M
M
a
a
n
1
n
⋅x
+ a
+ ...+ a
13
3
1,m-1
⋅x
+ a
+ ...+ a
23
3
2,m-1
⋅x
+ a
+ ...+ a
33
3
3,m-1
.
...
.
.
...
.
⋅x
+ a
+ ...+ a
2
n-1,3
3
n-1,m-1
⋅x
+ a
+ ...+ a
n3
3
n,m-1
L
a
1
m
L
a
2
m
x
,
O
M
L
a
2
nm
n
×
m
⋅x
⋅x
+ a
= b
,
m-1
1,m
m
1
⋅x
⋅x
+ a
= b
,
m-1
2,m
m
2
⋅x
⋅x
+ a
= b
,
m-1
3,m
m
3
.
.
.
.
⋅x
⋅x
+ a
= b
,
m-1
n-1,m
m
n-1
⋅x
⋅x
+ a
= b
.
m-1
n,m
m
n
×
n
x
b
1
1
x
b
2
2
b
,
M
M
x
b
m
n
m
×
1
× n
1
Page 11-16
⋅x
×
m
m
1