Exercise 33 illustrates how you can use the powers of a matrix to find its dominant eigenvalue (i.e., the eigenvalue with maximal modulus), at least when this eigenvalue is real. But what about the other eigenvalues?
a. Consider an
b. As an example of part a, consider the matrix
We wish to find the eigenvectors and eigenvalues of A without using the corresponding commands on the computer (which is. after all, a “black box”). First, we find approximations for the eigenvalues by graphing the characteristic polynomial (use technology). Approximate the three real eigenvalues of A to the nearest integer. One of the three eigenvalues of A is negative. Find a good approximation for this eigenvalue and a corresponding eigenvector by using the procedure outlined in part a. You are not asked to do the same for the two other eigenvalues.
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Linear Algebra With Applications (classic Version)
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