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matrixwolfram-mathematicadifferential-equations

Convert table to matrix equation

my table looks like this:

 {975/2048 - 512 y[1] + 256 y[2]},
 {175/128 + 256 y[1] - 512 y[2] + 256 y[3]},
 {4095/2048 + 256 y[2] - 512 y[3] + 256 y[4]},

I want to convert it to a matrix equation:

A*y=b

Do you have some suggestions to do it? Thanks!

Solution 
  • eq = {
     975/2048 - 512 y[1] + 256 y[2],
     175/128 + 256 y[1] - 512 y[2] + 256 y[3],
     4095/2048 + 256 y[2] - 512 y[3] + 256 y[4]} 
 b = -eq /. y[_] -> 0;
 a = Transpose[Table[ D[ eq, y[i]] , {i, 4}]];
 a.Table[ y[i], {i, 4}] == b

 {-512 y[1] + 256 y[2],
   256 y[1] - 512 y[2] + 256 y[3], 
   256 y[2] - 512 y[3] + 256 y[4]} == 
                {-(975/2048), -(175/128), -(4095/2048)}

    then to solve:

    sol = LinearSolve[a, b];

    {3155/524288, 5335/524288, 4715/524288, 0}

    (eq /. Table[ y[i] -> sol[[i]] , {i, 4}]) == {0, 0, 0}

    True