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.
I know that but for f(x)=f(-x) cant we just add the x of the opposite sign then it givesyou 0? And no I did not buy the textbook because I never needed textbooks for math..well until maybe now.
Where is a good site I can read the definition? Because I skipped all classes on vector spaces and my prof doesn't post notes online. And the prof only took off 0.5 points off for this question.
And I really have no clue how this works. Now I don't even know what the point of (af)(x)=a(f(x)) is
Well at the point where the function touches the y axes so x=0, then no matter what the sign is both f(x)=f(-x)= the same thing. So does it mean that the vertex point at the origin satisfies this?
I actually hav eno clue what the definition is, I kind of skipped the entire lecture on the vector space part, all I know it is similar with subspaces and etc. So I guess I have to just let this question go with marks taken off because it is due in 5 hours and its 4 am over here. Linear Algebra...
Homework Statement
Consider w= {f \in F(\Re|f(-x)=f(x) for all x \inR
Use the subspace test to verify W is a subspace of F(R)
Homework Equations
The Attempt at a Solution
0 is in W obviously
for closure under addition:
(f+g)(x) = (f+g)(-x) = f(x) +g(x) = f(-x)+g(-x)
I am...
Homework Statement
Let M2 denote the set of all 2x2 matrices. We define addition with the standard addition of matrices, but with scalar multiplication given by:
k \otimes [a b c d] = [ka b c kd] (note that they are matrices)
Where k is a scalar. Which of the...