system of linear equations

Hi Matlab experts I need to solve a system of linear equations nut the problem is far beyond my knowledge and I hope somebody here can help me to solve it. So here is the problem: I have 30,000 (or more) linear equations, and totally 15,000 unknowns. Each equation has 6 unknowns with the form aX1+bX2+cX3+dX4+eX5+fX6=0; I know as the number of equations is more than the number of the unknowns, the system will/may have multiple solutions. Neglecting the obvious solution which is zero (Xi=0), I am trying to find the best solution but still couldn't manage to do it.

If you have experiences with similar systems, would you please help me and give me advises to solve it.

[Matt J]

I know as the number of equations is more than the number of the unknowns, the system will/may have multiple solutions.

No, not if the matrix is full column rank. You're thinking of the case when there are fewer equations than unknowns.

Answer 1

[Roger Stafford]

It looks like a problem for the 'svd' (singular value decomposition) function where you select the vector that corresponds to the smallest singular value, but I don't know how well it would do with that large number of variables and equations. Certainly you would need to use the "economy" option.