Does anyone know how to do SVD back substitution in Matlab?

I am trying to do an Affine transformation: Xm = Xe*M, where Xm is the measured and Xe is the expected x,y coordinates (so, Xe,Xm are (n,2) matrix).

Normally, one would do: [U, S, V] = svd(Xe); then one would compute M via: M = svdBackSub(U, S, V, Xm);

Of course svdBackSub doesn't exist in Matlab. I am an old Igor Pro user which had this function. Is there anything equivalent in Matlab? Perhaps via using eigenvalue or inverse matrix functions.

Any help is appreciated.

[Matt J]

Is there a reason not to simply do

 M=Xe\Xm;