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## x = Z\z

 From: oort Subject: x = Z\z Date: Thu, 6 Jan 2011 15:08:39 -0800 (PST)

```Hello.

If x = Z\z is the solution of Zx=z and only square systems have solution
then why the operation of non-square matrices Z gives "numerical values"?
Don't you think that it should give some error message?

For instance:

octave:1> A = [3, 2, 6; 2, -2, 1; -1, 0.5, 3]
A =

3.00000   2.00000   6.00000
2.00000  -2.00000   1.00000
-1.00000   0.50000   3.00000

octave:2> a = [1; 2; 3]
a =

1
2
3

octave:3> A\a
ans =

-0.74684
-1.26582
0.96203

OK... "A" is a 3x3 matrice and "a" is a 3x1 matrice

But:

octave:4> B = [3, 2; 2, -2; -1, 0.5]
B =

3.00000   2.00000
2.00000  -2.00000
-1.00000   0.50000

octave:5> b = [1; 2; 3]
b =

1
2
3

octave:6> B\b
ans =

0.29801
-0.11479

Now we have a system of 3 equations and 2 variables. It's a overdefined
system. Curiously B*x does not give equal to "b"...

And if we use a underdefined system we aldo reach a "numeric" result.

octave:7> C = [3, 2, 6; 2, -2, 1]
C =

3   2   6
2  -2   1

octave:8> c = [1; 2]
c =

1
2

octave:9> C\c
ans =

0.42175
-0.51459
0.12732

How it is possible to have a "result" from a underdifined system?
Curiously  if we put a third row with zeros in C and if we calculate C*x we
obtain "c". However in octave x = [0.42175; -0.51459; 0.12732] and in MATLAB
x = [0; -0.7857; 0.4286]
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