Suppose we represent the input information as a (nx1) column vector, the output information as another (nx1) column vector and the system response function as a (nxn) matrix. My question, is it possible to calculate the values of the cells of the matrix knowing the input and the output? For example, if the known values of the input vector are multiplied by the first row of the matrix, we will get the first value of the output vector which is already known. To solve for n-values of the first row of the response function matrix, we need to repeat this process n-times using n-different values of inputs and outputs. Will this be possible?