Question

explain what meant by stating that the laplace transform is a linear transform... write down the two linear properties..

Answer 1

if a transform is a linear transform,
$$T(u+v)=T(u)+T(v)\\
T(ru)=rT(u)$$
where r is constants, u,v are vectors

so, laplace tansform is a transform of a function defined as
$$T[f(t)]=\int_0^\infty f(t)e^{-st}dt$$ in this case u(or v) that is stated previously is a function.

Check for the linearity.