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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
,,
831
532
3
2
1
⎥
⎦
⎤
⎢
⎣
⎡
−
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
−
−
= bxA and
x
x
x
.
22
5
15
,,
11
52
31
2
1
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
−= bxA and
x
x