1.6.101 Fields, Groups, Rings

condition: A homogeneous system of linear equations \( A X=0 \) is given \( \quad \) by the matrix \( A \). The elements of the matrix \(A\) belong to the field \(P\) of characteristic 0 or finite characteristic \(k\). Find all solutions of this system in each field \(P\). \[ A=\left(\begin{array}{cccc} -383 & 280 & -360 & -388 \\ 108 & -53 & 100 & 108 \\ -42 & 22 & -35 & -42 \\ 494 & -264 & 460 & 499 \end{array}\right) \]