1. The problem statement, all variables and given/known data Show that every linear operator L:ℝ→ℝ has the form L(x) = cx for some c in ℝ. 2. Relevant equations A linear operator in vector space V is a linear transformation whose domain and codomain are both V. 3. The attempt at a solution If L is a vector space of the real numbers to the real numbers, then I need to show that by multiplying any scalar to an element of the real numbers, then that will yield another real number in the domain of V. Well, assume to the contrary. That is, there exists a scalar c, such that c times an element x in ℝ, yields a number that is not in the reals. Well, the only c that would work is a number that is not contained in the ℝ. However, from hypothesis, c is in ℝ. Therefore, this is a contradiction. Does this seem right?