Chapter 1 - Linear Equations in Linear Algebra - 1.5 Exercises - Page 49: 39

Note that we can factor scalars out of equations; thus, $A(cu) = c(Au)$ We are given that $Au = 0$; thus, $A(cu) = c(Au) = c * 0 = 0$. Thus, we have shown $A(cu) = 0$ and that $cu$ also satisfied the equation $Ax = 0$.

Answer contains full explanation; see answer above.