Q: solving ax=0 with regularization?

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hi all,

I would like to solve a system of equations of the following form:

A_{nx9} X_{9x1} = 0_{nx1}

Where A is a matrix (known) obtained from a set of observation, and X (unknown) is a vector derived from some state variables. In fact, X is the Kronecker project of 2 unit vectors:

X = kron( a_{1x3},b_{1x3} )'

where |a| = |b| = 1.

Since A is constructed from a set of observations, each rows are not exactly independent of each other. In general, n>>9, and if I attempt to solve X by solving the null-space, I end up with basis functions that satisfies the equation, but not a particular solution.

From my limited knowledge of linear algebra (still reading upon it), I understand AX=0 could be solve using some iterative solver with regularization. My question is:

How can I solve AX=0 in matlab while using |a| = |b| =1 as a regularization term?

any help is very much appreciated,