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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Show that any two eigenvectors of the
|
|
−1 | 0 | −1 |
|
||
| 0 | −1 | 0 | ||||
| −1 | 0 | 3 |
Find the characteristic polynomial of 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)
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
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