Seymor says that multiplying a row by -1 preserves total unimodularity. Please explain this fallacy.
2026-03-25 08:10:55.1774426255
Consider the matrix {1, -1; 1 -1}. If I multiply first row by -1, it loses the total unimodular property.
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multiplying the matrix by $-1$, we obtain
$$\begin{pmatrix} -1 & 1 \\ 1 & -1 \end{pmatrix}.$$
Clearly, every $1$ by $1$ matrix is unimodular and the matrix itself is singular. Hence it is still totally unimodular.