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I want to solve the system $A - B = C$ to $A$, with $A$, $B$, $C$ matrices. And the variables in the matrix $B$ and $C$ are a combination of the variables in $A$. How can I do this? Because LinearSolve doesn't work in this case.

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You can use the Equate command to produce a set of equations that relation to the given elementwise equality.

For example, Equate(A-B, C).

Then you might use solve or fsolve on the set of equations that result from calling Equate.

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