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

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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.

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