# Linear Algebra: Linear Combinations

by lockedup
Tags: algebra, combinations, linear
 P: 70 1. The problem statement, all variables and given/known data Let V = {f: $$\mathbb {R}\rightarrow\mathbb {R}$$} be the vector space of functions. Are f1 = ex, f2 = e-x (both $$\in$$ V) linearly independent? 2. Relevant equations 0 = aex + be-x Does a = b = 0? 3. The attempt at a solution My first try, I put a = e-x and b = -ex. He handed it back and told me to try again. I think the problem was that my a and b were not constants. But how to prove that there are no constants that will make the equation 0? I wrote some stuff down about the fact that, if a=0, then b = 0 (and the converse). Is that sufficient or am I way off?
 Quote by lockedup 1. The problem statement, all variables and given/known data Let V = {f: $$\mathbb {R}\rightarrow\mathbb {R}$$} be the vector space of functions. Are f1 = ex, f2 = e-x (both $$\in$$ V) linearly independent? 2. Relevant equations 0 = aex + be-x Does a = b = 0?