(Real Math) Looking for a fancy matrix trick

All the same, I'd have to collect all the terms just to calculate A, B and C- how would I do it in general?

 

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See the pattern that emerges:

\(A+B+C=0\)
\(Aa_4+Ba_2+Ca_3=-1\)

 

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Ok, I'll play around a bit and see... You're suggesting I'll get a general pattern for all the coefficients A, B, C, D,... without having to work recursively? Can you show how the argument proceeds in the first example where you calculated A and B?

 

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Yes, I think so.

\(A+B=0\)
\(Aa_3+Ba_2=-1\)



\(A+B+C=0\)
\(Aa_4+Ba_2+Ca_3=-1\)


I think the next one emerges as:


\(A+B+C+D=0\)
\(Aa_5+Ba_4+Ca_3+Da_2=-1\)