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Solved: [M] In Exercises 19 and 20, find (a) the largest
Chapter 5, Problem 20E(choose chapter or problem)
[M] In Exercises 19 and 20, find
(a) the largest eigenvalue and
(b) the eigenvalue closest to zero. In each case, set \(\mathbf{x}_{0}=(1,0,0,0)\) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
\(A=\left[\begin{array}{rrrr}1 & 2 & 3 & 2 \\ 2 & 12 & 13 & 11 \\ -2 & 3 & 0 & 2 \\ 4 & 5 & 7 & 2\end{array}\right]\)
Questions & Answers
QUESTION:
[M] In Exercises 19 and 20, find
(a) the largest eigenvalue and
(b) the eigenvalue closest to zero. In each case, set \(\mathbf{x}_{0}=(1,0,0,0)\) and carry out approximations until the approximating sequence seems accurate to four decimal places. Include the approximate eigenvector.
\(A=\left[\begin{array}{rrrr}1 & 2 & 3 & 2 \\ 2 & 12 & 13 & 11 \\ -2 & 3 & 0 & 2 \\ 4 & 5 & 7 & 2\end{array}\right]\)
ANSWER:Solution 20EStep 1 The objective is to find the largest eigenvalue and the eigenvalue closest to zero for the following matrix: Use MATLAB to find the list.Code in MATLAB:function[x,lambda]=powermat(A,x0,nit) x = x0; for n=1:nit xnew = A*x; lambda = norm(xnew,inf)/norm(x,inf); fprintf('n = %4d lambda = %g x = %g %g %g \n', n, lambda, x'); x=xnew; end x=x/norm(x);%normalise x fprintf('n = %4d normalised x = %g %g %g\n', n, x');