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Suppose the 3 x 3 matrix A has eigenvalues A₁ = -6, A₂ = -2, and A3 = 5. (a) Let u be randomly chosen vector in R³. Set and for k> 0 set xo V ||v||' Xo = xo Axo Ark Fk+1 = Xk+1 ||Axk||¹ i. What number do you expect A to converge to? 1¹Axk+1 =Xk+1 ii. What number do you expect ||Ark - Akk|| to converge to? iii. For large k, , is approximately an eigenvector corresponding to which eigenvalue of A?

Suppose the 3 x 3 matrix A has eigenvalues A₁ = -6, A₂ = -2, and A3 = 5. (a) Let u be randomly chosen vector in R³. Set and for k> 0 set xo V ||v||' Xo = xo Axo Ark Fk+1 = Xk+1 ||Axk||¹ i. What number do you expect A to converge to? 1¹Axk+1 =Xk+1 ii. What number do you expect ||Ark - Akk|| to converge to? iii. For large k, , is approximately an eigenvector corresponding to which eigenvalue of A?

Advanced Engineering Mathematics
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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Suppose the 3 x 3 matrix A has eigenvalues A₁ = -6, A₂ = -2, and A3 = 5. (a) Let u be randomly chosen vector in R³. Set and for k> 0 set xo V ||v||' Xo = xo Axo Ark Fk+1 = Xk+1 ||Axk||¹ i. What number do you expect A to converge to? 1¹Axk+1 =Xk+1 ii. What number do you expect ||Ark - A|| to converge to? iii. For large k, æ, is approximately an eigenvector corresponding to which eigenvalue of A? (1) (2)
Transcribed Image Text:Suppose the 3 x 3 matrix A has eigenvalues A₁ = -6, A₂ = -2, and A3 = 5. (a) Let u be randomly chosen vector in R³. Set and for k> 0 set xo V ||v||' Xo = xo Axo Ark Fk+1 = Xk+1 ||Axk||¹ i. What number do you expect A to converge to? 1¹Axk+1 =Xk+1 ii. What number do you expect ||Ark - A|| to converge to? iii. For large k, æ, is approximately an eigenvector corresponding to which eigenvalue of A? (1) (2)
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