# When does a matrix equation have a solution? [closed]

Given a matrix equation $Ax=b$ where $A$ is a matrix and $b$ is a column vector, what is a condition that would ensure that there is a column vector $x$ that satisfies the equation?

Assume the dimensions are sensible, and feel free to provide multiple conditions.

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## closed as off-topic by Andres Caicedo, Jeremy Rouse, Alex Degtyarev, András Bátkai, Joe SilvermanMar 7 at 15:48

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about research level mathematics within the scope defined in the help center." – Andres Caicedo, Jeremy Rouse, Alex Degtyarev, András Bátkai, Joe Silverman
If this question can be reworded to fit the rules in the help center, please edit the question.

I assume you're looking for a condition considerably weaker than "A is invertible". –  Anton Geraschenko Oct 3 '09 at 14:49
I see that the research level considerably falls down. –  loup blanc Mar 7 at 15:33
@loupblanc Huh? This question is ancient. If one wants to see anything it might be that the level is higher than it was. (Or I missed your point completely.) –  quid Mar 7 at 18:28
@loupblanc This question was posted when MO was less than a month old, and the level of appropriate question had not at all be established. In fact, I was not asking the question because I needed to know the answer, but in a small effort to help populate the new site with questions. I would be quite satisfied to see this (and my other two questions) deleted, but I'll leave that question to folks that are active on the site. –  Eric Wilson Mar 7 at 20:42
Less than a week old. If memory serves, MathOverflow debuted on Sep. 28. –  The Masked Avenger Mar 8 at 5:25