Homework Statement
This is the last part of a revision question I'm trying, would really like to get to the end so any pointers or help would be greatly appreciated.
Suppose h:(0,1)-> satisfies the following conditions:
for all xЭ(0,1) there exists d>0 s.t. for all x'Э(x, x+d)n(0,1) we...
This is the last part of a problem that I'm working through. The problem is on Rolle's theorem.
Using Rolles Theorem prove that for any real number λ: the function f(x) = x^3 - (3/2)x^2 + λ never has two distinct zeros in [0,1].
So I was thinking about ways I could do this: but when I...
This is a revision problem I have come across,
I have completed the first few parts of it, but this is the last section and it seems entirely unrelated to the rest of the problem, and I can't get my head around it!
Suppose that the 2x2 matrix A has only one eigenvalue λ with eigenvector v...
I can sort of see it, but working on a proof right now. Will check back later if I get one out. For some reason I just don't see how this answers the question! Sorry for being a pain and thank you for your advice so far.
The only way I know how to find the length of a vector is by squaring and square-rooting. I have never used the transpose to find the length. Ahh I am very stuck!
Have been revising geometry today and have came across some proofs that I can't seem to find in books, but I can't get through either. Any help would be great.
Let A be a 3x3 orthogonal matrix and let x and y be vectors in R^3
a) Show that detA = +/- 1
b) Show that the length of Ax is...
Hello,
I am working through some examples for revision purposes and am pondering over this question so would appreciate any help I could receive.
I would like to prove that if T is a linear transformation on V such that T^2 = T, and I is the identity transformation on V,
i)Ker(T) =...
Yes! Sorry I am new so wasnt sure how this all worked!
Basically I think the first is false and the second true!
I think this because for the second one,
if i use the fact that an/bn →1
I can say that
|an-bn| = bn |an/bn -1| → 0 because bn is bounded.
I think this works?
I can't really...
True or False, with a proof or counterexample.
a) If bn ≠ 0 and an/bn →1, then an-bn → 0
b) If bn ≠ 0, bn is bounded and an/bn → 1 then an-bn → 0
At the moment I cannot even see which is false so I am struggling with this question. I think the proof will require use of the quotient...