# Extracting coefficient Matrix and vector from available polynomial Expressions with exponential terms

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Rajani Metri on 12 May 2019
Commented: Star Strider on 25 Mar 2021
Hello All,
I have stuck in one problem, where I have variable matrix vector available and I want to extract the coefficient matrix and variable vector from that original polynomial vector matrix. For e.g. if A is matrix as:
and I want to extract its coefficients and variable vector as given below:
So my question is how to compute or Extract Matrix Y and Matrix Z from A which comprises of expressions with exponential terms of eigenvalues of system matrix.
Is there any direct command? I tried commands like - coeffs, sysvar, equationsToMatrix but in all those cases the variables are fixed.
Thank You.

Star Strider on 12 May 2019
You have not shown what you already tried or what the results were.
In R2019a, this is possible with a for loop (since coeffs apparently doesn’t like matrices):
syms lambda1 lambda2 t
A = [exp(-lambda1*t)+3*exp(-lambda2*t); -2*exp(-lambda1*t)+4*exp(-lambda2*t)];
for k = 1:size(A,1)
[Ac{k},trm{k}] = coeffs(A(k,:));
end
Cfs = [Ac{1}; Ac{2}]
Trm = [trm{1}; trm{2}]
producing:
Cfs =
[ 1, 3]
[ -2, 4]
Trm =
[ exp(-lambda1*t), exp(-lambda2*t)]
[ exp(-lambda1*t), exp(-lambda2*t)]
That may be the best you can hope for.
Star Strider on 25 Mar 2021
As always, my pleasure!

Rajani Metri on 15 May 2019
If the coefficients of lyamda in A matrix are either 0 (ZERO) or if the eigenvalues are repeated then there will be t term along with exponential term (For e.g. e^(-2t) and t.e^(-2t). So in these two cases Z Matrix is not correctly computed.
Apart from these two cases the above program given by Star Strider work.
Thank You.