Is there an example of a real rank $2$ $\{0,1\}$ matrix of $4\times 4$ size with every row distinct and no zero rows? How to prove there is none if there is no example?
2026-04-01 04:16:38.1775016998
A certain example of matrix
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Hint Can you construct a $4 \times 2$ matrix with the same properties? (In particular, how many distinct $1 \times 2$ $(0, 1)$ matrices are there?)
Hint for edited post Pick two linearly independent rows of the matrix; since the rank of the matrix is $2$, all other rows are linearly combinations of these. Which linear combinations of the rows are nonzero and contain only $0$ and $1$ entries?