How to solve an equation of the form A (matrix) x(vector) = b(vector) and a constant c where I have to find x and c, and x is only positive?

Hi, I have a matrix A

A =[1 1 2 2 0 0;
    1 1 2 2 0 0;
    0 0 0 1 0 0;
    0 0 0 1 0 0;
    3 0 0 0 0 0;
    3 0 0 0 0 0;
    3 0 0 0 1 0;
    3 0 0 0 1 0;
    3 0 0 0 1 0;
    3 0 1 1 1 0;
    3 0 1 1 1 0;
    3 0 2 0 0 1;
    3 0 2 0 0 1];

and a vector b

b = [64.20; 42.60; 14.60; 5.75; 30.40; 27.20; 36.50; 25.40; 40.60; 38.90; 15.50; 38.40; 35.30];

if I use linesolve, I have

x =

      9.6000
     57.7333
    -17.1417
     10.1750
      5.3667
     42.3333

but negative values are nor realistic, I was planning to use linear programming but I'm not sure if is the way to go since I also need to have a constant (which can be negative) so I can have

Axc=b

Can you recommend me something?

Thanks!

Answer 1

[Star Strider]

If you want to avoid negative parameters, use the lsqnonneg function.

Example:

x = lsqnonneg(A,b)

x =
          9.6
       36.306
            0
       3.7469
       1.0813
         8.05

Answer 2

[KSSV]

Doc mldivide

[German Preciat Gonzalez]

hi, thanks but is the same answer than using: linesolve I need only positive values for x

[KSSV]

It is a linear equation...I has unique solution. How you expect only positive when negative solution is also possible.

[German Preciat Gonzalez]

that is why I want to use a constant C that multiplies vector x so the vector x can have only positive values: Axc=b

[KSSV]

C = [1 1 -1 1 1 1 1]';

But you should do element by element .* multiplication.