# (Real Math) Looking for a fancy matrix trick

I wasn't finished with the post, look up.

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?

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?

See the pattern that emerges:

$$A+B+C=0$$
$$Aa_4+Ba_2+Ca_3=-1$$

See the pattern that emerges:

$$A+B+C=0$$
$$Aa_4+Ba_2+Ca_3=-1$$

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?

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?

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:

$$A+B+C+D=0$$
$$Aa_5+Ba_4+Ca_3+Da_2=-1$$