Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector. 1 2 7 7 5 14 15 13 A = -5 2 0 5 9 4 8 2 a. The largest eigenvalue is approximately (Do not round until the final answer. Then round to four decimal places as needed.)

Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector. 1 2 7 7 5 14 15 13 A = -5 2 0 5 9 4 8 2 a. The largest eigenvalue is approximately (Do not round until the final answer. Then round to four decimal places as needed.)

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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Question

Find (a) the largest eigenvalue and (b) the eigenvalue closest to zero. In each case, set x, = (1,0,0,0) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
1 2 7 7
5 14 15 13
A =
-5 2 0 5
9 4 8 2
a. The largest eigenvalue is approximately
(Do not round until the final answer. Then round to four decimal places as needed.)

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The eigenvalues in this problem are all nonnegative. First determine whether A=0 is an eigenvalue; then find the positive eigenvalues and associated eigenfunctions. 7y +Ay=0; y(-x)=0, y(x)=0 Is A = 0 an eigenvalue of this problem? Select the correct answer below and, if necessary, fill in the corresponding answer box to complete your choice. OA. Yes, A-0 is an eigenvalue with the corresponding eigenfunction yo(x)= OB. No, when A=0 the only solution to the given equation is the trivial solution. OC. No, when A=0 there are an infinite number of nontrivial solutions to the give equation. What are the eigenvalues and eigenfunctions of the problem for n=1. 2. 3...? Select the correct answer below and fill in the corresponding answer box to complete your choice OA. The eigenvalues are À = OB. The eigenvalues are À = The eigenfunctions are yn(x)= The eigenfunctions are y(x) = regardless of whether n is even or odd when n is even and y(x) when n is odd.