HP 50g Graphing Calculator - Manual (Page 353)

Page 11-26
Under-determined system
Consider the system
2x
1
+ 3x
2
–5x
3
= -10,
x
1
– 3x
2
+ 8x
3
= 85,
with
The solution using LSQ is shown next:
Over-determined system
Consider the system
x
1
+ 3x
2
= 15,
2x
1
– 5x
2
= 5,
-x
1
+ x
2
= 22,
with
The solution using LSQ is shown next:
.
85
10
, ,
8 3 1
5 3 2
3
2
1
⎥
⎦
⎤
⎢
⎣
⎡−
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
= b x A
and
x
x
x
.
22
5
15
, ,
1 1
5 2
3 1
2
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
− = b x A
and
x
x