Problem with linear least squares, '\' does not work, Why ?

Hi,

I have really simple question that I have to accomplish. I have couple lines of equations, all I want to do is solve these by using least squares. Question is in the format;

x + y = 4
-2x + 4y = 11
5x - 11y = -21
3x - 13y = -29
-4x - 16y = -41

All looks ok... I already checked the documentation and found the function that will exactly solve this type of problems: mldivide, \

As it states on description "If A is a rectangular m-by-n matrix with m ~= n, and B is a matrix with m rows, then A\B returns a least-squares solution to the system of equations A*x= B"

I am getting some crazy results when I use this. Here is how I tried... to solve:

a = [1 1; -2 3; 5 -11; 3 -13; -4 -16]
b = [4; 11; -21; -29; -41]
x = a\b

The result is weird (or I don't know if I am missing something)

x

Outputs:

x =

     0.67992
     2.38273

And,

a * x

Outputs:

3.0626
5.7883
-22.8104
-28.9357
-40.8433

Answer 1

[Star Strider]

The key to understanding what the mldivide,\ function is doing here is ‘least-squares solution’.

You have an overdetermined system (more equations than unknowns), so mldivide computes a least-squares solution to your system.