# Matrix for zeroing specific entries.

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.

• 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? – Anton Grudkin Jun 8 '16 at 15:25
• Either side is fine. I'm just looking for $f$, where $f(A) = B$ , so $f(A) = X A$ would be fine. – Mark Cidade Jun 8 '16 at 15:38

If $a,b,\ldots,i$ are nice so the LHS is invertible, set $$X = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}^{-1} \begin{pmatrix} 0 & b & c \\ d & e & 0 \\ 0 & h & i \end{pmatrix}$$