Let R be an n n upper triangular matrix whose diagonal entries are all distinct. Let Rk denote the leading principal submatrix of R of order k, and set U1 = (1). (a) Use the result from Exercise 12 to derive an algorithm for finding the eigenvectors of R. The matrix U of eigenvectors should be upper triangular with 1s on the diagonal. (b) Show that the algorithm requires approximately n3 6 floating-point multiplications/divisions.

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