The eigenvalues of an upper triangular matrix are identically equal to:

(A) The diagonal elements of the matrix

(B) The elements of the first row

(C) The trace divided by the order of the matrix

(D) Zero for all triangular matrices

Answer Key:

A

### Solution: For any upper triangular, lower triangular, or diagonal matrix, det(A - \lambda I) is the product of (a_{ii} - \lambda), meaning the eigenvalues are exactly the principal diagonal entries. Correct: A.

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