How to find a 1x3 matrix with resultant as zero matrix in Matlab

Question

I know a 3x3 matrix M, and I want to find a 1x3 matrix P. The given condition is:

[p1 p2 p3]*[m11 m12 m13; m21 m22 m23; m31 m32 m33] = [0 0 0]

Given is [m11 m12 m13; m21 m22 m23; m31 m32 m33]

I have to find non trivial (non-zero) solution of [p1 p2 p3] using Matlab.

I am wanting to be done in Matlab because its part of a code. If needed, given also is a condition:
p1 + p2 + p3 = 1

P.S: I have tried the 'inv' function which gives the inverse of a matrix, however it is giving trivial solution. I have also read about the 'svg' and 'null' functions, but I doubt that they are meant for the Ax=B type, where as my problem is xA=B type.

Answer 1

Does Matlab have a function for calculating the kernel of a matrix? If so, you should be able to use that.

Looks like it does: http://www.mathworks.com/matlabcentral/newsreader/view_thread/45457

Answer 2

This problem Ax=b can be solved using the gaussian algorithm.