Answer
We are given that $Au = 0$ and $Av = 0$.
By the distributive property of matrices, $A(u+v) = Au + Av = 0 + 0 = 0$
We can similarly factor scalars out of matrix multiplication. Thus, $A(cu + cv) = A(cu) + A(cv) = c(Au) + c(Av) = c*0 + c* 0 = 0$
Therefore, we have proven $A(u+v) = 0$ and $A(cu + dv) = 0$.
Work Step by Step
Answer contains full explanation; see answer above.
