Give parametric solution of system of linear equations

If we have a system of linear equations like this:

S2 - S1 + S3 == 0

- S1 - S2 - S3 == 0

S1 - S2 - S3 == 0

How can we make MatLab give the solution?

As you can calculate for yourself, the solution will be parametric. In this case the solution will be:

t*[0; 1; -1] where t is a parameter.

When I try to use linsolve in MatLab, it says "Warning: System is rank deficient. Solution is not unique."

So how can we write to make matlab give the parametric solution? I.e. I want MatLab to write something similar to this:

t*[0; 1; -1]

How can we do that?

Answer 1

[Matt J]

I think you've mis-typed your example. The system of equations you've shown is nonsingular and therefore can only have a solution of [0;0;0].

    >> A=[1,-1, 1; -1,-1,-1; 1, -1, -1]

    A =

         1    -1     1
        -1    -1    -1
         1    -1    -1

    >> cond(A)

    ans =

        2.0000

Also, only 2 equations are needed to define a line such as you've shown.

However, For non-singular A, representing the homogeneous equations, you can get the parametric solutions numerically using null(A). It might be possible to do the same for symbolic equations as well.