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Category > Math Posted 22 Apr 2017 My Price 8.00

Math 636 - Assignment 9 - Written Component

Hi there,

Can you please help me with number 2 and 3 please?  Thank you so much!

 

 

Math 636 - Assignment 9 - Written Component
Due: Friday, July 15 at 4:00PM 2 3 1
1. Let A = 2 1 −1.
−2 3 5
(a) Find all of the eigenvalues of A and state their algebraic multiplicity.
(b) Find a basis for the eigenspace of each eigenvalue of A.
(c) Determine if A is diagonalizable. If it is, write a matrix P and a diagonal matrix D such that
P −1 AP = D. If it isn’t, explain why it isn’t. a b b b
b a b b 2. Let A = b b a b where b 6= 0. Prove that A is diagonalizable.
b b b a
3. Let ~n ∈ Rn , and let L : Rn → Rn be the linear mapping defined by
L(~x) = ~x − 2 ~x · ~n
~n,
k~nk2 for all ~x ∈ Rn (a) Show that if ~y ∈ Rn , such that ~y 6= ~0 and ~y · ~n = 0, then ~y is an eigenvector of L. What is its
eigenvalue?
(b) Show that ~n is an eigenvector of L. What is its eigenvalue?
(c) What are the algebraic and geometric multiplicities of all eigenvalues of L? 1

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ComputerScienceExpert
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Status NEW Posted 22 Apr 2017 05:04 AM My Price 8.00

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