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Solved: In Exercises 1–4, the matrix A is followed by a
Chapter 5, Problem 3E(choose chapter or problem)
QUESTION:
Problem 3E
In Exercises 1–4, the matrix A is followed by a sequence produced by the power method. Use these data to estimate the largest eigenvalue of A, and give a corresponding eigenvector.
Questions & Answers
QUESTION:
Problem 3E
In Exercises 1–4, the matrix A is followed by a sequence produced by the power method. Use these data to estimate the largest eigenvalue of A, and give a corresponding eigenvector.
ANSWER:
Solution 3E
Step 1
Consider the matrix,
And, the sequence produced by the power method is,
The sequence approaches.
So, the vector is probably the best estimate to find the eigenvalue.
Now,
The largest absolute entry in is.
So, the estimated eigenvalue of is
And, the corresponding eigenvector is,