Question: A common misconception is that if A has a strictly dominant eigenvalue, then, for any sufficiently large value of k, the vector Akx is approximately

A common misconception is that if A has a strictly dominant eigenvalue, then, for any sufficiently large value of k, the vector Akx is approximately equal to an eigenvector of A. For the three matrices below, study what happens to Akx when x = (.5, .5), and try to draw general conclusions (for a 2 x 2 matrix).
a.

2 9 5 2 0

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a Notice that A 5 x is approximately 8A 4 x Conclusion If the eigenvalues of A are all less ... View full answer

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