# How to find the Elements of a Coefficient Matrix?

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ercan duzgun on 11 Dec 2020
Answered: RUTUPURNA CHOUDHURY on 1 Sep 2021 at 13:55
How to find the matrix coefficients of an equation? For example think that we have an equation of "E=A+Ax^2+Bx+Cx+Cx^2+Ay+Ay^2+By^2". We might choose a row matrix of M=[1 x x^2 y y^2]' . In order to have E=N*M, what elements of N should be? (E is 1x1 matrix, M=5x1 matrix, N=1x5 matrix). (by using MATLAB symbolic toolbox)
Solution by hand:
E=(A)*x^0 + (B+C)*x^1 + (A+C)x^2 + (A)*y + (A+B)*y^2;
Therefore;
N=[A (B+C) (A+C) A (A+B)]; (The solution)
E=N*M=[A (B+C) (A+C) A (A+B)]*[1 x x^2 y y^2]' = A+Ax^2+Bx+Cx+Cx^2+Ay+Ay^2+By^2.

Sai Veeramachaneni on 14 Dec 2020
Hi,
You can leverage coeffs function to find coefficients of an equation.
Example-
syms A B C x y
E=A+A*x^2+B*x+C*x+C*x^2+A*y+A*y^2+B*y^2;
[N,M]=coeffs(E,[x y])
ercan duzgun on 14 Dec 2020
Dear Sai Veeramachaneni, thank you very much.

RUTUPURNA CHOUDHURY on 1 Sep 2021 at 13:55
How can we find the cofficient matrix from a non-linear equation ?
Note: Like equations to matrix command used for linear system of equatins. Like this what command used for non-linear equations?

R2020a

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