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LINEAR ALGEBRA!!! i need the complete and clear solutionplease, thanks.
Let V be the set of real-valued functions that are dened at each x in the interval (??,?). If ?f = f(x) and ?g = g(x) are two functions in V and k is any scalar, we define the operations of addition and scalar multiplication by ( ?f + ?g) (x) = f(x) + g(x) , (k ?f)(x) = kf(x) . Verify the Vector Space Axioms for the given set of vectors.
This question deals with vector sub-spaces. I know I need to demonstrate that 1.) V is not equal to 0, 2.) x,y = V -> x+y = V, and 3.) V is proportional to R, x = V -> is proportional to x = V. But I do not know where to start. Can someone give me a hand? The topic is Linear Algebra. Thank you in advance!
