MATLAB: Least square solution of linear system of equations

leastsquareMATLAB

i have homework about least square solution that i have a linear system of equation

x1 + x2 + x3 = 4

-2×1 + 2×2 + x3 = 6

x1 + x2 – 2×3 = 6

anyone know how to find least square solution of the least square solution in matlab?

(answer output must be in vector form(x1,x2,x3))

Best Answer

Although you should do your homework yourself I think I can help you : )

This problem could be solved with the backslash operator (or mldivide)

X = [1 1 1
    -2 2 1
    1 1 -2]; % These are the coefficients from your linear system
Y = [4
    6 
    6]; % these are the responses from your linear system
P = X\Y; % and P' would be your [x1,x2,x3]

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MATLAB: Place array in a matrix

Perhaps I'm misunderstanding but if

 x = [1.0000         0
      0.5000    1.0000
      0.5000    1.5000
           0   -1.0000
     -1.0000    1.0000
      0.5000   -1.0000];

which is a 6x2 array, then wouldn't

 x*x'

be the desired 6x6 array?

MATLAB: How to solve a system of linear equations with strict inequalities and equalities

Hi Terri,

Looks like it is not possible. You have

[F1;F2;F3] = [10 2 10
              15 20 8
               6 4 12] * [x1;x2;x3]
Now if F1-F2 > 0         ident2
   and F1-F3 > 0         ident3
   then 2*F1-F2-F3 > 0   ident4      necessary but not sufficient
but that last quantity is [2 -1 -1]*[F1;F2;F3]
= [2 -1 -1]*[10 2 10
             15 20 8
             6 4 12] * [x1;x2;x3];
= [-1 -20 0] * [x1;x2;x3]

and that quantity can't be greater than zero. If you had allowed equality with the F's

F1-F2 >= 0 and F1-F3 >= 0

then x1 = x2 = 0, x3 = 1 might have been possible but it gives

F1 = 10   F2 = 8   F3 = 12

which satisfies the equality-allowed version of ident4 but not the equality-allowed version of ident3. So it goes.

Best Answer

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MATLAB: Place array in a matrix

MATLAB: How to solve a system of linear equations with strict inequalities and equalities

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