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Is there a matrix, $X$, that can be solved-for here?

$ \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array}\right) X = \left( \begin{array}{ccc} 0 & b & c \\ d & e & 0 \\ 0 & h & i \end{array}\right) $

I want a given $3\times3$ matrix to be transformed into the one above, with $a,f,$ and $g$ eliminated.

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  • $\begingroup$ Is it principal for you to use transform by right-hand multiplying on the matrix $X$ or you may use a bit more complex transformation? $\endgroup$ – Anton Grudkin Jun 8 '16 at 15:25
  • $\begingroup$ Either side is fine. I'm just looking for $f$, where $f(A) = B$ , so $f(A) = X A$ would be fine. $\endgroup$ – Mark Cidade Jun 8 '16 at 15:38
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If $a,b,\ldots,i$ are nice so the LHS is invertible, set $$ X = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}^{-1} \begin{pmatrix} 0 & b & c \\ d & e & 0 \\ 0 & h & i \end{pmatrix} $$

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