I am trying to create a matrix X like in the attached image. I have the vectors x,y,z denoted as DE,DN,DZ respectively.

 Accepted Answer

That is straightforward, using the (:) addressing to create column vectors regardless of their original orientation:
X = [ones(size(DE(:))) DE(:) DN(:) DZ(:)];
If you also have your ‘g’ vector (all vectors must be the same length), calculate the ‘a’ coefficients as:
a = X\g(:);

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