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How can I recover $X$ from

\begin{equation} AX = B \end{equation}

when $A$ is a singular matrices?

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up vote 1 down vote accepted

In general you can't. For example, both vectors


are solutions to the system


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You can, however, look for e.g. the least-norm solution. – user7530 Jan 8 '13 at 3:20

For most matrix equations, actually there is a unique solution. You just assign variables to the contents of $X$ and solve. You will get a system of linear equations. The above example had multiple solutions because one of the equations was $0x+0y=0$, which is always true.

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