Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0 -1 0 -1 0 -1 0 3. Find the characteristic polynomial of A. | 11 - A| = 2³ - 2² - 62-4 Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁, 22, 23) = (-√5 + 1,−1,√5 +1 Find the general form for every eigenvector corresponding to ₁. (Use s as your parameter.) X1 = (0,0,s) X Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) (t,t,0) x2 = X Find the general form for every eigenvector corresponding to 23. (Use u as your parameter.) x3 = -u, -u,0) X

Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0 -1 0 -1 0 -1 0 3. Find the characteristic polynomial of A. | 11 - A| = 2³ - 2² - 62-4 Find the eigenvalues of A. (Enter your answers from smallest to largest.) (2₁, 22, 23) = (-√5 + 1,−1,√5 +1 Find the general form for every eigenvector corresponding to ₁. (Use s as your parameter.) X1 = (0,0,s) X Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) (t,t,0) x2 = X Find the general form for every eigenvector corresponding to 23. (Use u as your parameter.) x3 = -u, -u,0) X

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 36E
See similar textbooks
icon
Related questions
Question

Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal.

 
−1 0 −1
 
0 −1 0
−1 0 3

Find the characteristic polynomial of A.

 
?I − A
 
 = 
λ3−λ2−6λ−4
 
 
 



Find the eigenvalues of A. (Enter your answers from smallest to largest.)

(?1, ?2, ?3) = 
 
 
−√5+1,−1,√5+1
 
 
  
 



Find the general form for every eigenvector corresponding to 

?1.

 (Use s as your parameter.)

x1 = 
(s)
 
 
 



Find the general form for every eigenvector corresponding to 

?2.

 (Use t as your parameter.)

x2 = 
(t,t)
 
 
 



Find the general form for every eigenvector corresponding to 

?3.

 (Use u as your parameter.)

x3 = 
(−u,−u)
 
 
 
Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0 -1 0 -1 0 -1 0 3 Find the characteristic polynomial of A. | 21 - A| = 2³ 3 2³-2²-62-4 Find the eigenvalues of A. (Enter your answers from smallest to largest.) (λ₁, A2, 23) = ( -√√5 + 1,−1,√5 +1 Find the general form for every eigenvector corresponding to 1₁. (Use s as your parameter.) (0,0,s) X1 = X Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x₂ = (t,t,0) Find the general form for every eigenvector corresponding to 23. (Use u as your parameter.) X3 = (-u, -u,0) X
Transcribed Image Text:Show that any two eigenvectors of the symmetric matrix corresponding to distinct eigenvalues are orthogonal. -1 0 -1 0 -1 0 -1 0 3 Find the characteristic polynomial of A. | 21 - A| = 2³ 3 2³-2²-62-4 Find the eigenvalues of A. (Enter your answers from smallest to largest.) (λ₁, A2, 23) = ( -√√5 + 1,−1,√5 +1 Find the general form for every eigenvector corresponding to 1₁. (Use s as your parameter.) (0,0,s) X1 = X Find the general form for every eigenvector corresponding to 12. (Use t as your parameter.) x₂ = (t,t,0) Find the general form for every eigenvector corresponding to 23. (Use u as your parameter.) X3 = (-u, -u,0) X
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS