I was wondering the following. Given a totally unimodular matrix $A$ and a vector $b \in Im(A)$ is then the matrix $[A,b]$ totally unimodular too? My guess is no, since for total unimodilarity every subdeterminant has to be +1,-1 or 0 and the subvector $b'$ extracted from $b$ might not be linearly independent with the columns of the submatrix $A'$ of $A$, but I was unable to find a counterexample.
2026-03-25 12:49:14.1774442954
Does adding linearly dependent columns to a totally unimodular matrix preserve total unimodilarity?
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