Transformations of equations into a matrix form

Question

I have a system of 4 equations which is the following :

CL1 = A2 + A4 == 0

CL2 = A1 + A3 == 0

CL3 = A2 Cos[L/lambda] + A1 Sin[L/lambda] ==  A4 Cosh[L/lambda] + A3 Sinh[L/lambda]

CL4 = A1 Cos[L/lambda] == A3 Cosh[L/lambda] + A2 Sin[L/lambda] + A4 Sinh[L/lambda]

I would like to transform into a system in the form A*X = 0

with X a vector (or list) like

X = {A1,A2,A3,A4}

May you help me to do this transformation that is to say to transform linear equation in a linear matrix form?

Answer 1

You can use CoefficientArrays

cArray = CoefficientArrays[{CL1, CL2, CL3, CL4}, {A1, A2, A3, A4}] // Normal;
cArray[[2]] // MatrixForm

$\begin{pmatrix} 0 & 1 & 0 & 1 \\ 1 & 0 & 1 & 0 \\ \sin \left(\frac{L}{\text{lambda}}\right) & \cos \left(\frac{L}{\text{lambda}}\right) & -\sinh \left(\frac{L}{\text{lambda}}\right) & -\cosh \left(\frac{L}{\text{lambda}}\right) \\ \cos \left(\frac{L}{\text{lambda}}\right) & -\sin \left(\frac{L}{\text{lambda}}\right) & -\cosh \left(\frac{L}{\text{lambda}}\right) & -\sinh \left(\frac{L}{\text{lambda}}\right) \\ \end{pmatrix}$