Is it possible to find matrix A satisfying certain conditions?

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Homework Statement
Is it possible to find A being a m by n matrix, and two vectors b and c, such that Ax = b has no solution and ##A^T## y = c has exactly one solution? Explain why.
Relevant Equations
Maybe Rank
Since Ax = b has no solution, this means rank (A) < m.

Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m

Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning?

Thanks
 
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songoku said:
Homework Statement: Is it possible to find A being a m by n matrix, and two vectors b and c, such that Ax = b has no solution and ##A^T## y = c has exactly one solution? Explain why.
Relevant Equations: Maybe Rank

Since Ax = b has no solution, this means rank (A) < m.

Since ##A^T y=c## has exactly one solution, this means rank (##A^T##) = m

Since rank (A) ##\neq## rank (##A^T##) so matrix A can not exist. Is this valid reasoning?

Thanks
Looks ok to me.
 
Thank you very much fresh_42
 
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