Finding coefficients and constant for multivariable linear equation.

Hello

I want to find the coefficients and constant for the equation: A*x_1 + B*x_2 + C*x_3 + D*x_4 + E = 0, using 4 given points that satisfies the equation.

How do you do this in Matlab? I tried using regress and only got the trivial solution A=B=C=D=E=0.

Thanks in advance!

Answer 1

[Shashank Prasanna]

Shelley, to find a non-trivial solution you have to find the null space of your data matrix.

You data matrix with a column of ones (for the intercept term E):

>> M = [[1,1,1,1; 2,3,2,2; 4,5,4,6; 0,1,3,4],[1;1;1;1]]

M =

     1     1     1     1     1
     2     3     2     2     1
     4     5     4     6     1
     0     1     3     4     1

Regress will give you the trivial solution that is zeros. Since M above is rank deficient there are a family of solutions. The non-trivial solution would be the null space which you can compute as follows:

>> null(M)

ans =

     -0.3536
      0.3536
     -0.7071
      0.3536
      0.3536

[Shelley]

Okay I got it now. Thank you very much

Answer 2

[bym]

You don't have enough points. 4 points < 5 unknowns

[Shelley]

Okay I see. Then there must be some kind of constraint for the equation that makes it possible to find a uniqe solution. The points are: (1,1,1,1), (2,3,2,2), (4,5,4,6), (0,1,3,4) and the equation is for an affine space in R^4.

Anybody knows how to solve this?