## Finding coefficients and constant for multivariable linear equation.

### Shelley (view profile)

on 25 Apr 2013
Accepted Answer by Shashank Prasanna

### Shashank Prasanna (view profile)

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.

### Tags ### Shashank Prasanna (view profile)

Answer by Shashank Prasanna

### Shashank Prasanna (view profile)

on 26 Apr 2013

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

### Shelley (view profile)

on 26 Apr 2013
Okay I got it now. Thank you very much

### bym (view profile)

on 25 Apr 2013

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

Shelley

### Shelley (view profile)

on 26 Apr 2013
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?