1.6.101 Fields, Groups, Rings

Condition: a homogeneous system of linear equations \ (a x = 0 \) set \ (\ quad \) matrix \ (a \). The elements of the matrix \ (a \) belong to the field \ (p \) characteristics 0 or the final characteristic \ (k \). Find all the solutions of this system in each field \ (p \). \ [A = \ Left (\ Begin {Array} {CCC} -383 & 280 & -360 & -388 \\ 108 & -53 & 1008 \\ -42 & 22 & -35 & -42 \\ 494 & -264 & 460 & 49999 \ end {Array} \ Right) \]