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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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2 Answers 2

up vote 1 down vote accepted

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

$$\,X_1=\binom{1}{0}\;\;,\;\;X_2=\binom{1}{1}$$

are solutions to the system

$$A_1=\begin{pmatrix}1&0\\0&0\end{pmatrix}\binom{x}{y}=\binom{1}{0}$$

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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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