Use the power method to approximate the dominant eigenvalue and eigenvector of A. Use th e given initial vector x0 , th e specified number of iterations k, and three-decimal-place accuracy.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Expert Solution
Step 1
The given matrix is and initial vector is and number of iteration
The power method for approximating eigenvalues is iterative. First let assume that the matrixAhas a dominant eigenvalue with corresponding dominant eigenvectors. Then choose an initial approximationof one of the dominant eigenvectorsofA. This initial approximation must be anonzerovector inRn. Then find
Step 2
First multiply the given matrix with the given initial matrix .
Now take common out of this matrix it becomes:
Step 3
Now find
Find
Now multiply by gives:
Take common from the matrix gives:
Now for third iteration as from the above process find
Now multiply with
Take common from the above matrix gives:
Step 4
Now find
Now multiply with
Take common from the above matrix gives:
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