Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors (1), v V₁ = v₂ = (3) och V3 = Let v = x1v1 + x2v2 + x3v3 be a linear combination of the three eigenvectors. (a) Which 3-vectors can be written as a linear combination of the three eigenvectors? (b) What A¹v₁, Av2, Av3 respectively Av? (n is an arbitrary integer) (c) What about Any when n→ ∞o? (It depends a little on the coefficients x1, x2, x3) (d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R
Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors (1), v V₁ = v₂ = (3) och V3 = Let v = x1v1 + x2v2 + x3v3 be a linear combination of the three eigenvectors. (a) Which 3-vectors can be written as a linear combination of the three eigenvectors? (b) What A¹v₁, Av2, Av3 respectively Av? (n is an arbitrary integer) (c) What about Any when n→ ∞o? (It depends a little on the coefficients x1, x2, x3) (d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors
(1), v
V₁ =
v₂ =
(3) och V3 =
Let v = x1v1 + x2v2 + x3v3 be a linear combination of the three eigenvectors.
(a) Which 3-vectors can be written as a linear combination of the three eigenvectors?
(b) What A¹v₁, Av2, Av3 respectively Av? (n is an arbitrary integer)
(c) What about Any when n→ ∞o? (It depends a little on the coefficients x1, x2, x3)
(d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5b2190e5-e9f6-4aa6-b00c-2b845039dd29%2F0a14fcaf-871a-492a-bb77-09d62ec9aa19%2Fn36kgo2_processed.png&w=3840&q=75)
Transcribed Image Text:Assume that a 3 x 3 matrix A has eigenvalues 21 = 1, 22=0.8, 23=0.6 With corresponding eigenvectors
(1), v
V₁ =
v₂ =
(3) och V3 =
Let v = x1v1 + x2v2 + x3v3 be a linear combination of the three eigenvectors.
(a) Which 3-vectors can be written as a linear combination of the three eigenvectors?
(b) What A¹v₁, Av2, Av3 respectively Av? (n is an arbitrary integer)
(c) What about Any when n→ ∞o? (It depends a little on the coefficients x1, x2, x3)
(d) Now suppose that we have a 3×3 matrix with some eigenvalues 21, 22, 23 € R
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