# multiplicity

1. ### Zero and Multiplicity

For the given polynomial function, list each zero and its multiplicity. f(x) = [x - (1/3)]^2*(x - 1)^3 The zero of a function is the value that makes the function zero, right? I am not too clear on the idea of multiplicity.
2. ### Question regarding multiplicity

Hi all, I'm hoping you can give me some homework help so I can better understand this question. I was asked, given a 0.05 significance level, how many of the 20 significance tests in the example I could expect to be significant by chance alone. I worked this out to be 1. (Correct?) In the...
3. ### Multiplicity of Functions

What is the multiplicity of functions in simple words?
4. ### roots with multiplicity > 1 polynomials

I was solving the problem listed here.. Polynomial x I understood the logic behind the first line which says that "A root is of multiplicity 1 ==> the polynomial has a root in common with it's own derivative. But I wasn't able to follow the next where the reply is like this. Thus the given...
5. ### Need Help. Polynomials and multiplicity

Can someone help me with the problem. I need to understand it. I'm having a hard time creating the polynomial. The roots of multiplicity and the x=2 and x=0 are throwing me off. Where are they getting these from??? Here is the question: The polynomial of degree 5, has leading coefficient...
6. ### Multiplicity Homework Problem

Hi, I was wondering if I could have help with the following problem: Let A be an n by n matrix and let lambda be an eigenvalue of A whose eigenspace has dimension k, where 1<k<n. Show that lambda is an eigenvalue of A with multiplicity at least k. I'm supposed to use the following theorem...
7. ### Determine multiplicity

Determine the multiplicity for the root z = 1 for f(z)=(1-cos2\pi z)^{30} How exactly?
8. ### eigen value geometric multiplicity problem

find the jordan form of A=\left(\begin{array}{cccc} 4 & 1 & 1 & 1\\ -1 & 2 & -1 & -1\\ 6 & 1 & -1 & 1\\ -6 & -1 & 4 & 2\end{array}\right) ? my latex around the matrices is not working and it meesed up the whole thing so i removed it |tI-A|=\left|\begin{array}{cccc} t-4 & -1 & -1 & -1\\ 1...
9. ### eigenvalues --- multiplicity

ImageShack® - Online Photo and Video Hosting I found the 3 eigenvalues to be 1, 2 and -2. But how do I find which of the eigenvalues have multiplicity greater than 1? The only way i know is to calculate it (A-lambdaI), but is there some other way? Thanks
10. ### Algebraic and Geometric multiplicity

let A be the matrix |4 1 0 0 0| |0 4 1 0 0| |0 0 4 1 0| |0 0 0 4 1| |0 0 0 0 4| I am asked to find the algebraic multiplicity and the geometric multiplicity I think as it is an upper triangular matrix eigenvalues are the diagonal entries i.e. all 4, 4^5 so Am is 5, im not sure on the geometric...
11. ### Eigenvalue with multiplicity of 2?

haha im an idiot, i got it figured out
12. ### Multiplicity Problem.

I've been trying to figure out how to do this, but all the book says is... "In mathematics, we distinguish the difference between the solutions to this last equation (x^3-4x^2-3x+18=0) and the equation x^2-x-6=0 by saying x=3 is a solution of multiplicity 2 in the equation x^3-4x^2-3x+18=0...
13. ### State the multiplicity of each zero

Find the zeros of the polynomial function and state the multiplicity of each zero: P(x)=x^2 (3 x+5)^2 So I know that x=-5/3 but sense things are squared I'm loosing the picture. Is it 0 (multiplicity of 2) and -5/3 (multiplicity of 2)?
14. ### Characteristic roots problem

I am almost completely lost with this problem. I say almost completely because i have a vague understanding of the principle but my professor rushed through this lecture and our text book doesnt cover this.(Crying) Here is the problem: Prove that every solution of the equation: y'' + a1y' +...
15. ### Multiplicity of a root

Let c be a fixed real number. Show that a root of the equation x(x+1)(x+2)...(x+2009)=c can have multiplicity at most 2. Determine the number of values of c for which the equation has a root of multiplicity 2. Can anybody tell me how to compute this?
16. ### factor polynomial and state the multiplicity

how do i factor this completely to find the zeros and then state the multiplcity of each zero?? p(x)= x^3-x^2+x
17. ### Estimating local maxima and minima and identifying multiplicity of factors. #2

estimate the local maxima and minima and identify the mulltiplicity of the factors 1) F(X)=(2X^2+2X-4)(X^2-6X+9)
18. ### Estimating local maxima and minima and identifying multiplicity of factors #1

estimate the local maxima and minima and identify the mulltiplicity of the factors. 1) F(X)=X^2(x+2)^2(X-5)
19. ### Euler's phi function: multiplicity

I am supposed to show that, for Euler's totient function: a.) If n is an odd integer, then \phi(2n)=\phi(n). and b.) If n is an even integer, then \phi(2n)=2\phi(n). I thought I would use the multiplicity of phi to establish this, i.e. \phi(2n)=\phi(2)\cdot\phi(n)=1\cdot\phi(n)=\phi(n)...
20. ### The arithmetic and geometric multiplicity of an eigenvector

I have a matrix and I am supposed to calculate the eigenvalue, eigenvector and then give arithmetic and algebraic multiplicity.I can calculate the eigenvalues and the eigenvectors but I don't know how to calculate the arithmetic and geometric multiplicity. Tried to google it but it was a bit...