2. Compute the eigenvalues and eigenvectors of each of the following matri- ces. 0 1 -1 1 0 -1 0 2 0 0 1 -2 0 0
2. Compute the eigenvalues and eigenvectors of each of the following matri- ces. 0 1 -1 1 0 -1 0 2 0 0 1 -2 0 0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
Related questions
Question

Transcribed Image Text:ATH-5342 X
FIL
PDF
Jackson and Ginsburg 2008 p X
Ontent/uploads/sites/16915/2018/04/linalg.pdf
O
0
1
+
0
Figure 2.1.3. Action of the transformation (2.1.15) on R2, with a dou-
ble eigenvalue and one-dimensional eigenspace
2. Compute the eigenvalues and eigenvectors of each of the following matri-
ces.
BAB =
-1
0
2
0
-1
0
W linalg.pdf
2
1
-2
0
A₁
CD A DO
3. Let A E M(n. C). We say A is diagonalizable if and only if there exists
an invertible BE M(n. C) such that BAB is diagonal:

Transcribed Image Text:Show that this is also given by
det (AIA) =
n
k=0
where do(A1,..., An) = 1, and, for 1 ≤ k ≤n,
O
k=1
σκ(λι,..., λη) = Σ Aj₁ Ajk
1<<...<jk ≤n
The polynomials ok are called the elementary symmetric polynomials.
64
(-1) kok(A₁,..., An)λ¹-k,
8. If A, B E M(n, C), B invertible, and D = B-¹AB, show that, for all
KEN,
D = B-¹A B.
i
9. Let A denote the first matrix in Exercise 2. Diagonalize A and use this
to compute
A100
2. Eigenvalues, eigenvectors, and generalized eigenvectors
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