I have always been lazy to the "statements", never thought they were really important, unless it is the conclusion other than that the answer is pretty obvious. In calculus questions for integrals and derivative questions like rate of change and etc. I never put Let x be that so I almost always...
Ok, I was confused on what you guys meant by "vector" I thought the entire f(x) is considered a vector. and when it comes to the zero vector I was confused on whether the "f(x)" is the vector or the (x), so I was completely off. If this continues I think I am going to kill my brain, maybe I need...
So my last response what do you have to say in the answer? DO you just have to say the zero vector is in f(x)=f(-x) as f(x)=0? I just dont know how to shwo your work? As I am not good with showing every step, like you said you have to say "for all x" or w.e. I lost all my marks on communications...
I thought f(x) was the vector ? So do I have to say f(x) = 0 is the zero vector and belongs to the subspace since f(x)=f(-x)? I am not exactly sure how to answer this question. How is f a vector? I am so confused, this is so different from what we learned before I took this course. It is more...
WHy does that matter!? Why are we looking at examples? no the second one does not satisfy all x. it is not a vectorspace at all. :). But how does this matter? I want ot know how to proof that whether 0 is in the space or not.
So (f+0)(x)=f(x)+0(x)=f(x)=f(-x) work?
Believe it or not I do have a good mark in it. But what is the zero vector? I know that x+y=x. But for f(x)=f(-x) what is a zero vector for this? f(x)+g(x)=f(-x)? so g(x)=0? or does the value x in g(x) is 0? How is 1 in f(x)=f(-x) when your example is : x^2 + x + 1/2? f(1)=2.5 and f(-1)=0.5...
And it does not touch the x axis therefore it will not work. But I still dont see the point of this. I think the examples and the definitions are irrelevant. So what if it says x+y=x then why do we still need to proof that it is in f(x)=f(-x) ? of course there is an x that f(x+y=x) = f(-x+y=-x)...
no that is not in the set...for example 1 would not work. You guys kept on repeating the same thing and I do not understand that thing. I dont know any thing and I have no idea what thing you are talking about either. I think I need to go drop this course or drop myself down a building and suicide.