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 don't 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...
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 don't 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 don't 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) can't 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...
I got something like T(r+2s, -2r+s, 3r-s) = (r+s, 2r, 3r-s, 4r) Then the answer could be A. But how do you actually do the question how tdo you solve that? I just did by guessing and inputing numbers to get one of the choices (A-F).
Homework Statement
Let T: R3--> R4 be a linear transformation. Assume that T(1,-2,3) = (1,2,3,4), T(2,1,-1)=(1,0,-1,0)
Which of the following is T(-8,1-3)?
A. (-5,-4,-3,-8)
B. (-5,-4,-3,8)
C. (-5,-4,3,-8).
D.(-5,4,3,-8)
E (-5,4,-3,8)
F. None of the above.
Homework Equations
I really have no...
Homework Statement
True/False: If true give a proof, if false give a counterexample.
a)
If A and B have the same eigenvector X, then A+B should also have the same eigenvector, X.
b)
if A has an eigenvalue of 2, and B has an eigenvalue of 5, then 7 is an eigenvalue of A+B...
How do you tell if it is diagonalizable or not? It is a 3x3 matrix so... I am not sure. I can find a invertible matrix, but how do you know if it is diagonalizable?
1 1
0 1
That is from an example that teacher gave us. But how do you know the eigenvectors without constructing examples and checking everytime? How to tell what the eigenvectors are by just the matrix itself?
Homework Statement
For each of the following, give an example if it exists. If it doesn't exist, explain why.
a) An invertible 3x3 matrix which is not diagonalizable.
c) An 3x3 matrix A with A^6+I3=0 (Hint: Use the determinant)
Homework Equations
For a):
I know in order for a...
I think c fits, since it says Ax=0 has a unique solution, but it may be different from the solution to ax=b. What you said there I know, but I think my english is horrible and did not understand the problem. Because when it said it may be different from the solution to Ax=b, i thought it also...
Homework Statement
Suppose we know that a linear system Ax = b has a unique solution. What can we say about the solutions of the linear system Ax = 0?
a) It has the same solution.
b) The solution to Ax = b is also a solution to Ax=0, but there may be other solutions.
c) Ax = 0 has a...